Soumyarup Banerjee

activity

20162026

most citedExplicit identities on zeta values over imaginary quadratic field

3 citations · 9 across the 14 of their papers we have counts for

collaborators

17 papers

math.NT2026

Hecke-type action on higher order Herglotz-Zagier function

Soumyarup Banerjee, Riya Mandal

In a seminal paper, Lewis and Zagier constructed variety of functions satisfying the three-term functional equations. In this article, we consider the first example among them and…

math.NT2024

Sums of generalized polygonal numbers of almost prime "length"

Soumyarup Banerjee, Ben Kane, Daejun Kim

In this paper, we consider sums of three generalized $m$ -gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions o…

math.NT2023★ 1 cited

A note on odd zeta values over any number field and Extended Eisenstein series

Soumyarup Banerjee, Rajat Gupta, Rahul Kumar

In this article, we have studied transformation formulas of zeta function at odd integers over an arbitrary number field which in turn generalizes Ramanujan's identity for the Riem…

math.NT2023

Explicit transformations for generalized Lambert series associated with the divisor function $σ_{a}^{(N)} (n)$ and their applications

Soumyarup Banerjee, Atul Dixit, Shivajee Gupta

Let $σ_{a}^{(N)} (n) = \sum_{d^{N} ∣ n} d^{a}$ . An explicit transformation is obtained for the generalized Lambert series $\sum_{n = 1}^{\infty} σ_{a}^{(N)} (n) e^{- n y}$ for Re $(a) > - 1$ using the…

math.NT2022★ 1 cited

Transformation formulas for the higher power of odd zeta values and generalized Eisenstein series

Soumyarup Banerjee, Vijay Sahani

In this article, we obtain a transformation formula for the higher power of odd zeta values, which generalizes Ramanujan's formula for odd zeta values. We have also investigated ma…

math.NT2022

Lambert series of logarithm, the derivative of Deninger's function $R (z)$ and a mean value theorem for $ζ (\frac{1}{2} - i t) ζ^{'} (\frac{1}{2} + i t)$

Soumyarup Banerjee, Atul Dixit, Shivajee Gupta

An explicit transformation for the series $n = 1 \sum \infty \frac{lo g ( n )}{e ^{n y} - 1},$ Re $(y) > 0$ , which takes $y$ to $1/ y$ , is obtained for the first time. Th…

math.NT2022

On a Conjecture of Sun about sums of restricted squares

Soumyarup Banerjee

In this paper, we investigate sums of four squares of integers whose prime factorizations are restricted, making progress towards a conjecture of Sun that states that two of the in…

math.NT2021

Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms

Soumyarup Banerjee, Rahul Kumar

In this article, we obtain transformation formulas analogous to the identity of Ramanujan, Hardy and Littlewood in the setting of primitive Maass cusp form over the congruence subg…

math.NT2021★ 1 cited

Finiteness theorems for universal sums of squares of almost primes

Soumyarup Banerjee, Ben Kane

In this paper we study quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway--Schneeberger 15 theorem.

math.NT2021

Number field analogue of divisor function à la Koshliakov

Soumyarup Banerjee, Rahul Kumar

In this article, we study a divisor function in an arbitrary number field akin to Koshliakov's work on Vorono\"{\dotlessi} summation formula. More precisely, we generalize Koshliak…

math.NT2021★ 3 cited

Explicit identities on zeta values over imaginary quadratic field

Soumyarup Banerjee, Rahul Kumar

In this article, we study special values of the Dedekind zeta function over an imaginary quadratic field. The values of the Dedekind zeta function at any even integer over any tota…

math.NT2020

Piltz divisor problem over number fields à la Voronoï

Soumyarup Banerjee

In this article, we study the Piltz divisor problem, which is sometimes called the generalized Dirichlet divisor problem, over number fields. We establish an identity akin to Voron…

math.NT2019

Fermat's polygonal number theorem for repeated generalized polygonal numbers

Soumyarup Banerjee, Manav Batavia, Ben Kane +5

In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain t…

math.AG2018

Ansatz for $(- 1)^{n - 1} \nabla p_{n}$

Soumya Dipta Banerjee, Mahir Bilen Can, Adriano Garsia

We construct a special family of equivariant coherent sheaves on the Hilbert scheme on $n$ -points in the affine plane. The equivariant Euler characteristic of these sheaves are clo…

math.NT2016

An analogue of Wilton's formula and values of Dedekind zeta functions

Soumyarup Banerjee, Kalyan Chakraborty, Azizul Hoque

J. R. Wilton obtained an expression for the product of two Riemann zeta functions. This expression played a crucial role to find the approximate functional equation for the product…

math.NT2016

A Note On Signs Of Fourier Coefficients Of Two Cusp Forms

Soumyarup Banerjee

Kohnen and Sengupta proved that two cusp forms of different integral weights with real algebraic Fourier coefficients have infinitely many Fourier coefficients of the same as well…

math.KT2016★ 3 cited

Equivariant $K$ -theory of smooth projective spherical varieties

S. Banerjee, Mahir Bilen Can

We present a description of the equivariant $K$ -theory of a smooth projective spherical variety. This provides an integral $K$ -theory version of Brion's calculation of equivariant…

Hecke-type action on higher order Herglotz-Zagier function

Sums of generalized polygonal numbers of almost prime "length"

A note on odd zeta values over any number field and Extended Eisenstein series

Explicit transformations for generalized Lambert series associated with the divisor function σa(N)​(n) and their applications

Transformation formulas for the higher power of odd zeta values and generalized Eisenstein series

Lambert series of logarithm, the derivative of Deninger's function R(z) and a mean value theorem for ζ(21​−it)ζ′(21​+it)

On a Conjecture of Sun about sums of restricted squares

Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms

Finiteness theorems for universal sums of squares of almost primes

Number field analogue of divisor function à la Koshliakov

Explicit identities on zeta values over imaginary quadratic field

Piltz divisor problem over number fields à la Voronoï

Fermat's polygonal number theorem for repeated generalized polygonal numbers

Ansatz for (−1)n−1∇pn​

An analogue of Wilton's formula and values of Dedekind zeta functions

A Note On Signs Of Fourier Coefficients Of Two Cusp Forms

Equivariant K-theory of smooth projective spherical varieties

Explicit transformations for generalized Lambert series associated with the divisor function $σ_{a}^{(N)} (n)$ and their applications

Lambert series of logarithm, the derivative of Deninger's function $R (z)$ and a mean value theorem for $ζ (\frac{1}{2} - i t) ζ^{'} (\frac{1}{2} + i t)$

Ansatz for $(- 1)^{n - 1} \nabla p_{n}$

Equivariant $K$ -theory of smooth projective spherical varieties