Monday, July 20, 2026
A. Satyanarayana Reddy (Shiv Nadar University) - Thursday, July 2, 2026 - 4:00 PM (IST)
Talk Announcement:
Title: A Gateway to the Circle Method: Ramanujan Sums and the Ternary Goldbach Problem
Speaker: A. Satyanarayana Reddy, Shiv Nadar University.
When: July 2, 2026, 4:00 PM- 5:00 PM IST
Link: https://youtube.com/live/MSXP_YYzNWA?feature=share
Abstract:
The Ramanujan sum is a fundamental exponential sum possessing deep arithmetic and orthogonality properties. In this talk, we first establish these classical properties, then use them as a gateway to understand the Hardy-Littlewood Circle Method. We will see how additive problems like the Ternary Goldbach Conjecture are translated into integrals of exponential sums.
Saturday, June 13, 2026
Rishabh Sarma (Penn State University) - Thursday, June 18, 2026 - 6:00 PM (IST)
Dear All,
The talk in the coming week will be delivered by Rishabh Sarma, S. Chowla Research Assistant Professor of the Department of Mathematics at Pennsylvania State University.
Talk Announcement:
Title: Modular symmetries for rank and crank statistics
Title: Modular symmetries for rank and crank statistics
Speaker: Rishabh Sarma, Pennsylvania State University.
When: June 18, 2026, 6:00 PM- 7:00 PM IST
When: June 18, 2026, 6:00 PM- 7:00 PM IST
Where: Zoom: Write to the SFNT organizers.
Abstract
Let R(z,q) be the two-variable generating function for Dyson’s rank function. In his lost notebook Ramanujan gives the p-dissection of R(ζp,q) where ζp is a primitive p-th root of unity and p=5. This result is related to Dyson’s famous rank conjecture which was proved by Atkin and Swinnerton-Dyer. In this talk, we explore the modular structure of this function, the partition crank and their overpartition counterparts, leading to a symmetry phenomenon among the elements of the p-dissection of these functions.
--
Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia
Special Functions and Number Theory Seminar
Wednesday, May 27, 2026
Yashovardhan Singh Gautam (IIT, Roorkee) - May 28, 2026, 4:00 PM- 5:00 PM IST
Dear all,
The next talk is tomorrow, by Yashovardhan Singh Gautam of IIT, Roorkee. I apologize for the late notification.
There is also an announcement.
Bibekananda Maji (IIT, Indore) and Manjil Saikia (Ahmedabad University) have joined us as co-organisers of the SF and NT Seminar. Their interests are in Combinatorics, Number Theory and Partitions. Both have spoken in the seminar previously.
Talk Announcement:
Title: On special values of Koshliakov zeta functions
Title: On special values of Koshliakov zeta functions
Speaker: Yashovardhan Singh Gautam, Indian Institute of Technology, Roorkee, India
When: May 28, 2026, 4:00 PM- 5:00 PM IST
Where: Zoom. Write to sfandnt@gmail.com for the link
Abstract
In this talk, we study the Koshliakov zeta function ηp(s), whose theory appears to be more involved than that of its counterpart ζp(s), owing to the fact that its defining series is not of Dirichlet type. We derive formulas for ηp(s) at both even and odd values of s. In the limiting case p → ∞, our results yield the celebrated formulas of Euler and Ramanujan for the Riemann zeta function. Moreover, our results lead to several consequences concerning closed-form expressions for Lambert series and their arithmetic properties, recovering results due to Berndt, Cauchy, Ramanujan, and others. We also propose p-analogues of the transformation formula for the classical Eisenstein series. Moreover, we introduce two families of p-analogues of Ramanujan polynomials and establish functional equations satisfied by them.
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Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia
Special Functions and Number Theory Seminar
Sunday, May 10, 2026
Nargish Punia (IIT, Roorkee) - Thursday, May 14, 2026 - 4:00 PM (IST)
Dear all,
The talk this week is by Nargish Punia of IIT, Roorkee.
Talk Announcement:
Title: On Partition classes arising from parity, differences and repeated smallest parts
Title: On Partition classes arising from parity, differences and repeated smallest parts
Speaker: Nargish Punia, Indian Institute of Technology, Roorkee, India
When: May 14, 2026, 4:00 PM- 5:00 PM IST
When: May 14, 2026, 4:00 PM- 5:00 PM IST
Where: Zoom: Write to the organisers at sf and nt at gmail.com for the link
Live Link: https://youtube.com/live/BMrnfrIzjxs?feature=share
Abstract
In this talk, we present various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions with a repeated smallest part. We establish identities connecting these various classes of partitions. Moreover, we will discuss how these identities help us to extend the Euler’s partition theorem. If time permits, we will also present an analogue of Legendre’s theorem of the partition-theoretic interpretation of Euler’s pentagonal number theorem. This is joint work with Rahul Kumar.
--
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Tuesday, February 17, 2026
Nikita Kalinin (Guangdong Technion, China) -- Thursday February 19, 2026 - 4:00 PM (IST)
Dear all,
The talk this week is by Nikita Kalinin, Guangdong Technion Israel Institute of Technology, Shantou, China.
Talk Announcement:
Title: Evaluation of lattice sums via telescoping over topographs
Title: Evaluation of lattice sums via telescoping over topographs
Speaker: Nikita Kalinin, Guangdong Technion Israel Institute of Technology, Shantou, China.
When: Feb 19, 2026, 4:00 PM- 5:00 PM IST (1830 Beijing Time)
When: Feb 19, 2026, 4:00 PM- 5:00 PM IST (1830 Beijing Time)
Where: Zoom: write to the organsers for the link
Abstract
Conway’s topograph provides a geometric way to organize values of binary quadratic forms on an infinite trivalent planar tree. In this talk, I explain how summation over vertices and edges of a topograph leads to a systematic method for evaluating a broad class of lattice sums by telescoping.
The main idea is that many arithmetic sums indexed by primitive lattice points or Farey-type data admit a natural decomposition along oriented edges of the topograph. When written in this form, local identities at each vertex produce global cancellations, yielding exact closed formulas depending only on the root configuration and the discriminant. This viewpoint unifies and simplifies several known identities, including sums related to reciprocal products of quadratic form values, Mordell–Tornheim–type series, and formulas connected to Euler-type constants.
The talk will be largely elementary and geometric. I will introduce the necessary background on topographs, explain the telescoping mechanism in a concrete way, and illustrate how classical analytic identities emerge from purely combinatorial summation over the tree.
The talk is based on https://arxiv.org/abs/2510.
The talk is based on https://arxiv.org/abs/2510.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Sunday, February 8, 2026
Sudhir Kumar Pujahari (NISER) - Thursday, February 12, 2026 - 4:00 PM (IST)
Dear all,
The next talk is by Sudhir Kumar Pujahari of the National Institute of Science Education and Research (NISER), Bhubaneswar, India.
Talk Announcement:
Title: Moments of the Trace of Frobenius in Arithmetic Progressions.
Title: Moments of the Trace of Frobenius in Arithmetic Progressions.
Speaker: Sudhir Kumar Pujahari, NISER (Bhubaneshwar, India)
When: Feb 12, 2026, 4:00 PM- 5:00 PM IST
When: Feb 12, 2026, 4:00 PM- 5:00 PM IST
Where: Zoom: Write to the organisers for the link.
Abstract
The statistical distribution of the trace of Frobenius for elliptic curves is a central theme in arithmetic geometry, famously encapsulated by the Sato–Tate conjecture. In this talk, we investigate the moments of the trace of Frobenius for elliptic curves over finite fields when the traces are constrained to a fixed arithmetic progression. We establish the asymptotic behavior of the moment as the size of the finite field tends to infinity. In the process, we will see a bridge between moments of traces of Frobenius and the theory of binary quadratic forms; specifically, we will derive these results from new asymptotic formulas for sums of Hurwitz class numbers restricted to arithmetic progressions. This talk is based on joint work with Ben Kane and Kathrin Bringmann.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Friday, January 16, 2026
Ramanujan Special: Dennis Stanton (Minnesota) - Thursday, January 22, 2026 - 7:30 PM- 8:30 PM IST (8 AM CST)
Happy new year.
The first talk of the year (on Jan 22, 2026) is a ``Ramanujan Special". This year's speaker is Dennis Stanton, who has decided to gift us a very special talk, containing several interesting open problems. Please note that the talk will be later than usual.
Talk Announcement: The 2026 Ramanujan Special
Title: Some open problems
Title: Some open problems
Speaker: Dennis Stanton, University of Minnesota
When: Jan 22, 2026, 7:30 PM- 8:30 PM IST (8 AM CST) (Note special time)
When: Jan 22, 2026, 7:30 PM- 8:30 PM IST (8 AM CST) (Note special time)
Abstract
I will discuss some open problems in q-series, partitions,
orthogonal polynomials, basic hypergeometric functions, and combinatorics, including the Rogers-Ramanujan identities.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Sunday, December 14, 2025
Aritram Dhar (Florida) -- Thursday December 18, 2025 - 4:00 PM (IST)
Dear all,
We have a talk this week by Aritram Dhar, of the University of Florida. The title and abstract are below.
Talk Announcement:
Title: Extension of Bressoud's generalization of Borwein's conjecture, some exact results, and applications
Title: Extension of Bressoud's generalization of Borwein's conjecture, some exact results, and applications
Speaker: Aritram Dhar (University of Florida)
When: December 18, 2025, 4:00 PM- 5:00 PM IST
Where: Zoom. Write to the organisers for a link
Abstract:
In this talk, we conjecture an extension of Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative q-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Using certain positivity-preserving transformations for q-binomial coefficients due to Berkovich and Warnaar, we prove the non-negativity of the infinite families. Time permitting, we present some applications of cubic positivity-preserving transformations where we establish new identities analogous to Andrews' representations of the Borwein polynomials. This is based on recent joint works with Alexander Berkovich.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Tuesday, October 21, 2025
Hussein Mourtada (Paris-Diderot) - Thursday, October 23 , 2025 - 4:00 PM IST (12:30 PM CEST)
Dear all,
We have a talk this week by Hussein Mourtada of the Université de Paris (Campus Paris-Diderot). The title and abstract are below.
Talk Announcement:
Title: Integer partitions, (hyper)graphs and monomial ideals
Title: Integer partitions, (hyper)graphs and monomial ideals
Speaker: Hussein Mourtada (Université de Paris (Campus Paris-Diderot))
When: October 23, 2025, 4:00 PM- 5:00 PM IST (12:30 PM CEST)
Where: Zoom: Please ask the organisers for a link
Abstract:
We will present new partition identities that are, in a certain sense, dual to Gordon’s identities. These results arise from a correspondence between three classes of objects: a new family of partitions (called neighborly partitions), monomial ideals, and certain infinite (hyper)graphs. This talk is based on joint works, one with Zahraa Mohsen and another with Pooneh Afsharijoo.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Sunday, October 12, 2025
Jehanne Dousse (Geneva) - Thursday, October 16 , 2025 - 4:00 PM (IST)
Dear all,
The talk next week is by Jehanne Dousse of the University of Geneva. The title and abstract are below.
There was a snafu in the previous talk organisation. Some announcements/reminders were inadvertently not sent. The video of the talk by Ritwik Pal (IIIT, Delhi) has been uploaded on sfandnt website.
Talk Announcement:
Title: Andrews-Gordon-Bressoud type identities and particle motion
Title: Andrews-Gordon-Bressoud type identities and particle motion
Speaker: Jehanne Dousse (University of Geneva)
When: October 16, 2025, 4:00 PM- 5:00 PM IST (12:30 PM CEST)
Abstract:
The Andrews-Gordon identities are among the most important q-series and partition identities, and generalise the famous Rogers-Ramanujan identities. Interestingly, while the product side of these identities clearly corresponds to partitions with congruence conditions, it is not obvious that the sum side of the q-series version is the generating function for the partitions with frequency conditions that appear in the combinatorial version. It was originally proved by George Andrews using recurrences, and then bijectively by Ole Warnaar using particle motion.
In this talk, we will explain and generalise the particle motion approach. We will show that the generalised version can be applied to the sum side of Bressoud's identity and that, using the Andrews-Gordon and Bressoud identities as starting points, it can prove many known and new identities.
This is based on joint work with Jihyeug Jang, Frédéric Jouhet and Isaac Konan.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Saturday, September 20, 2025
Ritwik Pal (IIIT, Delhi) - Sept 25, 2025 - 4:00-5:00 PM IST
Dear all,
This week's talk is by Ritwik Pal of the Indian Institute of Information Technology (IIIT), Delhi. The announcement is below.
Talk Announcement:
Title: On shifted convolution sum of Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke–Maass forms.
Title: On shifted convolution sum of Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke–Maass forms.
Speaker: Ritwik Pal (IIIT, Delhi)
When: Sept 25, 2025, 4:00-5:00 PM IST
Where: Zoom: Write to the organisers for a link
Abstract:
We will present a brief overview of the shifted convolution sum problems, especially those related to the coefficients of automorphic L-functions. Then we will present our recent article on establishing a non-trivial upper bound for the Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke–Maass forms. As a consequence, it gives a significant improvement over the previously known range of shifts for which a non-trivial upper bound of shifted convolution sum holds. This is a joint work with Sampurna Pal.
Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,
Special Functions and Number Theory Seminar
Sunday, September 7, 2025
Michael Schlosser (University of Vienna) - Thursday, Sept 11 , 2025 - 4:00 PM (IST)
Dear all,
Welcome back from the summer break. We hope you had an exciting summer, filled with new theorems and fresh collaborations.
The first talk of the season is by Michael Schlosser on Sept 11. The announcement is below.
Talk Announcement:
Title: Asymptotic formulas for the Fourier coefficients
of infinite $q$-products
Title: Asymptotic formulas for the Fourier coefficients
of infinite $q$-products
Speaker: Michael Schlosser (University of Vienna)
When: Sept 11, 2025, 4:00 PM- 5:00 PM IST (12:30 PM CEST)
Where: Zoom: (Write to the organisers for a link)
Abstract:
We derive asymptotic expansions for weighted partition
numbers satisfying certain conditions. As applications we
partially settle some conjectures by Berkovic and Garvan,
and by Seo and Yee, on the nonnegativity of the coefficients
of certain infinite products, and a conjecture by Chan and
Yesilyurt on the periodicity of the signs of the coefficients of
a non-theta product. This is joint work with Nian Hong Zhou.
numbers satisfying certain conditions. As applications we
partially settle some conjectures by Berkovic and Garvan,
and by Seo and Yee, on the nonnegativity of the coefficients
of certain infinite products, and a conjecture by Chan and
Yesilyurt on the periodicity of the signs of the coefficients of
a non-theta product. This is joint work with Nian Hong Zhou.
Sunday, May 18, 2025
Pranjal Talukdar (Tezpur University) - Thursday, May 22, 2025 - 4:00 PM (IST)
The talk this week is by Pranjal Talukdar of Tezpur university. Here is the announcement of the talk.
Talk Announcement:
Title: On the least $r$-gaps in partitions and identities for the Rogers-Ramanujan Continued fraction
Title: On the least $r$-gaps in partitions and identities for the Rogers-Ramanujan Continued fraction
Speaker: Pranjal Talukdar (Tezpur University)
When: May 22, 2025, 4:00 PM- 5:00 PM IST
Where: Zoom: Please write to the organisers for a link
Best wishes,
Gaurav Bhatnagar, Atul Dixit and Krishnan Rajkumar (organisers)
Abstract:
The minimal excludant of a partition $\pi=(\pi_1,\pi_2,\ldots,\pi_k)$ of $n$ is the smallest positive integer that is not present in $\pi$ and is denoted by $\textup{mex}(\pi)$. The least $r$-gap of $\pi$ is the least positive integer that does not appear in the partition at least $r$ times. In the first half of the talk, we derive some arithmetic functions related to the sum of least $r$-gaps. Using a Tauberian theorem due to Ingham, we obtain Hardy-Ramanujan-type asymptotic formula for two such functions. We also briefly mention some arithmetic properties for these functions.
In the second half, we prove some new identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then
\begin{align*}&R(q)R(q^4)=\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+R(q^{5})+R(q^{20})},\\
&\dfrac{1}{R(q^{2})R(q^{3})}+R(q^{2})R(q^{3})= 1+\dfrac{R(q)}{R(q^{6})}+\dfrac{R(q^{6})}{R(q)}.
\end{align*}
The contents of the talk is taken from two chapters of the speaker's Ph.D. thesis completed under the supervision of Prof. Nayandeep Deka Baruah at Tezpur University, India.
Tuesday, May 6, 2025
Abdulhafeez Abdulsalam (University of Ibadan and ICTP, Italy) - Thursday, May 8, 2025 - 4:00 PM (IST)
Dear all,
This week's talk is by Abdulhafeez Abdulsalam (University of Ibadan, Nigeria and ICTP, Italy). Here is the announcement.
Talk Announcement:
Title: Fourier sine and cosine transforms of expressions with nested square roots
Title: Fourier sine and cosine transforms of expressions with nested square roots
Speaker: Abdulhafeez Abdulsalam, University of Ibadan, Nigeria and ICTP, Italy
When: May 8, 2025, 4:00 PM- 5:00 PM IST (12:30 PM CET)
When: May 8, 2025, 4:00 PM- 5:00 PM IST (12:30 PM CET)
Where: Zoom: Please write to the organisers for a link
Live LInk: https://youtube.com/live/4_6SukI6IJ0?feature=share
Best wishes,
Gaurav Bhatnagar, Atul Dixit and Krishnan Rajkumar (organisers)
Abstract
We begin by applying the Laplace transform to derive closed forms for several challenging integrals that seem nearly impossible to evaluate. Using the solution to the Pythagorean equation a^2 + b^2 = c^2, we find that these closed forms become even more intriguing. This approach enables us to propose new integral representations for the error function, with some of the resulting formulas appearing as Fourier sine and cosine transforms.
Sunday, April 6, 2025
Krishnan Rajkumar (JNU, Delhi) - Thursday, Apr 10, 2025 - 4:00 PM
Dear all,
This week's talk is by Krishnan Rajkumar of Jawaharlal Nehru University (JNU), Delhi. Here is the announcement.
Talk Announcement:
Title: Telescoping continued fractions for several of Ramanujan's entries
Title: Telescoping continued fractions for several of Ramanujan's entries
Speaker: Krishnan Rajkumar (JNU, Delhi)
When: April 10, 2025, 4:00 PM- 5:00 PM IST (Our usual time)
When: April 10, 2025, 4:00 PM- 5:00 PM IST (Our usual time)
Where: Zoom:
Live LInk: https://youtube.com/live/eVgu2PvtG7U?feature=share
Abstract
We will recall earlier work where Apéry's proof of irrationality of ζ(3) was related to a continued fraction in Ramanujan's notebooks. We will then recall the method of Telescoping continued fractions from joint work with Bhatnagar (2023). We will then proceed to apply this method to certain series to prove several entries from Ramanujan's notebooks related to π, ζ(2), ζ(3) and G, the Catalan's constant.
Best wishes,
Gaurav Bhatnagar, Atul Dixit and Krishnan Rajkumar (organisers)
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