Debopam Chakraborty (BITS Pilani, Hyderabad)-Thursday, Oct 1, 2026 - 5:00 PM (IST)

 Dear All,

The talk this week will be delivered by Debopam Chakraborty from BITS Pilani, Hyderabad. 

Talk Announcement:
Title:  Supersingular Isogeny Graphs: A Glimpse into Post-Quantum Cryptography

Speaker: Debopam Chakraborty (BITS Pilani). 
When: October 1, 2026, 5:00 PM- 6:00 PM IST 

Where: Zoom: Write to the organisers for the link

Live Link: https://youtube.com/live/b38R4SzW1QM?feature=share

Abstract: Elliptic curve cryptosystem (ECC) has been an integral part of the current cryptographic protocols. ECC exploits the group structure of the solutions of an elliptic curve, resembling its similarity to RSA cryptography. On the other hand, supersingular isogeny graphs, associated with a more advanced cryptosystem based on isogenies between elliptic curves, were introduced as part of post-quantum cryptographic protocols. In this elementary talk, we introduce such graphs, related arithmetic properties, including their relation to ideal class groups of number fields, and various other properties.

Abdulhafeez Abdulsalam - Thursday, Sep 17, 2026 - 5:00 PM (IST)

 The talk today will be delivered by Abdulhafeez Abdulsalam, one of the 2022 Spirit of Ramanujan Fellows.

Talk Announcement:
Title: Signed Generalized Stirling Polynomials, Nested Sums, and Hyperbolic Secant Integral Identities
Speaker: Abdulhafeez Abdulsalam
When: September 17, 2026, 5:00 PM- 6:00 PM IST (1:30 PM CEST)
Where: Zoom: 
Live Link: https://youtube.com/live/x0JJhTMq1_s?feature=share

Abstract: We study signed generalized Stirling polynomials $P_k(m,x)$ arising in closed forms for Malmsten-type hyperbolic secant integrals. Their product structure is used to prove recurrences, gamma--polygamma formulas for $P_{m-s}(m,x)$, a central vanishing identity, a finite approximation to $\cosh \pi x$, and a limit formula for $\pi$. We identify these polynomials as signed residues of the equal-period Barnes multiple zeta function, derive their reflection formula, and obtain finite parity-cancellation and Stirling cycle-number identities, including a comparison with a classical Meixner--Pollaczek orthogonal family. We also evaluate finite nested sums built from the sequence $\chi_n$. Fixing the lower bounds turns these sums into coefficient-counting problems: common lower bounds give binomial coefficients and staircase bounds give Catalan numbers. Combining these counts with known formulas for $\chi_j$ yields explicit hyperbolic-secant integral evaluations involving Catalan's constant, zeta values,and polygamma values. A Wolfram Language package accompanies the formulas. This work is joint with Michael Schlosser.

Carsten Schneider (RISC, Johannes Kepler University, Linz, Austria) - Thursday, Sep 10, 2026 - 5:00 PM (IST)

 Dear All,

The talk today will be delivered by Carsten Schneider, a Professor in the Research Institute for Symbolic Computation (RISC) and Johannes Kepler University, Linz, Austria. 

Talk Announcement:
Title: Symbolic Summation and Applications in Number Theory and Elementary Particle Physics

Speaker: Carsten Schneider (RISC and Johannes Kepler University, Linz, Austria). 
When: September 10, 2026, 5:00 PM- 6:00 PM IST (1:30 PM CEST)

Where: Zoom: Write to the organisers

Live Link: https://youtube.com/live/zLobCavbPnI?feature=share

Abstract: In this talk I will present the general summation theory of difference rings and will sketch the underlying algorithmic ideas in this setting for telescoping, creative telescoping and recurrence solving. Special emphasis is put on concrete applications coming from number theory and QCD.

Thank you.

With kind regards,

--

Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia

Special Functions and Number Theory Seminar

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Michael Schlosser (University of Vienna) - Thursday, August 20, 2026 - 5:00 PM (IST)

 Dear All,

The next talk will be delivered by Michael Schlosser, Department of Mathematics at the University of Vienna. Please note the changed time for the coming semester. 

Talk Announcement:
Title: Bilateral $q$-ultraspherical functions

Speaker: Michael Schlosser (University of Vienna). 
When: August 20, 2026, 5:00 PM- 6:00 PM IST 

Where: Zoom: Write to the organisers for the link

Live Link: https://youtube.com/live/7gd61c0dDmw?feature=share

Abstract: We introduce the bilateral $q$-ultraspherical functions $C_n(x;\beta,\gamma|q)$ (where $n$ can be any integer), a bilateral-series extension of the continuous $q$-ultraspherical polynomials $C_n(x;\beta|q)$ (where $n$ is a nonnegative integer). They are defined by specific bilateral basic hypergeometric $_2\psi_2$ series, are analytic in the variable $x=\cos\theta$, and depend on two parameters $\beta$ and $\gamma$ and on a base $q$. Our main results for the bilateral $q$-ultraspherical functions $C_n(x;\beta,\gamma|q)$ include full orthogonality relations with respect to explicit orthogonality functionals involving analytic mass aggregates, which we establish by analytic continuation. Other results satisfied by the $C_n(x;\beta,\gamma|q)$ include a product formula for their bilateral generating function, a three-term recurrence relation, their transformation under the Askey--Wilson divided difference operator, Rodrigues-type formulae, and explicit large-order asymptotic expansions. We also obtain shifted orthogonality relations and a bilateral Chen--Liu type mixed orthogonality formula. In the limit $\gamma\to 1$, our results for the bilateral $q$-ultraspherical functions $C_n(x;\beta,\gamma|q)$ reduce to classical results for the continuous $q$-ultraspherical polynomials $C_n(x;\beta|q)$. Full details are given in https://arxiv.org/abs/2508.08908v2

Mithun Kumar Das (NISER) - Thursday, August 6, 2026 - 4:00 PM (IST)

The talk today will be delivered by Mithun Das, an Inspire Faculty of the Department of Mathematics at NISER, Bhubaneswar. 

Talk Announcement:
Title: Equidistribution: where Number Theory meets Analysis

Speaker: Mithun Kumar Das, NISER.
When: August 6, 2026, 4:00 PM- 5:00 PM IST 

Where: Zoom: Write to the organisers for the link.

Live Link:https://youtube.com/live/TWTLG8z4nRU?feature=share

Abstract: The theory of equidistribution has a long and rich history. Although its study originated in number theory, it soon became clear that equidistribution problems extend far beyond their number-theoretic roots. In this talk, we will explore how the equidistribution of algebraic numbers can be understood through the lens of Fourier analysis. 

This talk is based on an AIM group project (2021) and a recent joint work with Emanuel Carneiro (ICTP).

Bittu Chahal (IIT Indore) - Thursday, July 23, 2026 - 4:00 PM (IST)

 Dear All,

The talk of this week will be delivered by Bittu Chahal, a post-doctoral fellow of the Department of Mathematics at IIT Indore. 

Talk Announcement:
Title: Spacing statistics of the Farey sequence

Speaker: Bittu Chahal, IIT Indore.
When: July 23, 2026, 4:00 PM- 5:00 PM IST 

Where: Zoom:

Live Link: https://youtube.com/live/ttGMGYzpdOs?feature=share

Abstract:

The Farey sequence $\mathcal{F}_Q$ of order $Q$ is the ascending sequence of fractions $a/b$ in the unit interval $(0,1]$ such that $\gcd(a,b)=1$ and $0<a\leq b\leq Q$. The study of the Farey sequence is of independent interest because of its role in the Diophantine approximation, the circle method, and its connection to the Riemann Hypothesis, as established by the classical work of Franel and Landau. In this talk, we discuss the spacing statistics of the Farey sequence by studying equidistribution and correlation measure. In particular, we establish an estimate for the corresponding Weyl sum and explore whether correlation measure is Poissonian or non-Poissonian.

Thank you.

With kind regards,

--

Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia

Special Functions and Number Theory Seminar

A. Satyanarayana Reddy (Shiv Nadar University) - Thursday, July 2, 2026 - 4:00 PM (IST)

The talk this week is by A. Satyanarayana Reddy, Associate Professor of the Department of Mathematics at Shiv Nadar University. 

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 

Where: Zoom

Live 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. 

--

Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia

Special Functions and Number Theory Seminar

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

Speaker: Rishabh Sarma, Pennsylvania State University.
When: June 18, 2026, 6:00 PM- 7:00 PM IST 

Where: Zoom: Write to the SFNT organizers.

Live Link: https://youtube.com/live/6F-TG4LKkkg?feature=share

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(ζ_p,q) where ζ_p 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

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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

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

Live Link: https://youtube.com/live/ubCNCfyP1VI?feature=share

Abstract

In this talk, we study the Koshliakov zeta function η_p(s), whose theory appears to be more involved than that of its counterpart ζ_p(s), owing to the fact that its defining series is not of Dirichlet type. We derive formulas for η_p(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.

--

Gaurav Bhatnagar, Atul Dixit, Bibekananda Maji, Krishnan Rajkumar, and Manjil Saikia

Special Functions and Number Theory Seminar

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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

Speaker: Nargish Punia, Indian Institute of Technology, Roorkee, India
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

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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

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)

Where: Zoom: write to the organsers for the link

Live Link: https://youtube.com/live/iHy9UHCdBV8?feature=share

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/2510.02082 and  https://arxiv.org/abs/2510.00012 

Gaurav Bhatnagar, Atul Dixit, and Krishnan Rajkumar,

Special Functions and Number Theory Seminar

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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.

Speaker: Sudhir Kumar Pujahari, NISER (Bhubaneshwar, India)
When: Feb 12, 2026, 4:00 PM- 5:00 PM IST 

Where: Zoom: Write to the organisers for the link.

Live Link: https://youtube.com/live/dgnGN7RX9tA?feature=share

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

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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 

Speaker: Dennis Stanton, University of Minnesota
When: Jan 22, 2026, 7:30 PM- 8:30 PM IST (8 AM CST) (Note special time) 

(IST= CST + 11:30)

Where: Zoom: Please write to sfandnt@gmail.com for the link.

Live Link: https://youtube.com/live/6ui6EMf4qJs?feature=share

Download presentation. 

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

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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

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

Live Link: https://youtube.com/live/1-GzIoCJtBM?feature=share

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

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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

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

Live Link: https://youtube.com/live/iSTlKqaEC44?feature=share

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

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