3 citations · 9 across the 14 of their papers we have counts for
15 papers · 1 filter
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…
Sums of generalized polygonal numbers of almost prime "length"
Soumyarup Banerjee, Ben Kane, Daejun Kim
In this paper, we consider sums of three generalized -gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions o…
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…
Explicit transformations for generalized Lambert series associated with the divisor function and their applications
Soumyarup Banerjee, Atul Dixit, Shivajee Gupta
Let . An explicit transformation is obtained for the generalized Lambert series for Re using the…
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…
Lambert series of logarithm, the derivative of Deninger's function and a mean value theorem for
Soumyarup Banerjee, Atul Dixit, Shivajee Gupta
An explicit transformation for the series Re, which takes to , is obtained for the first time. Th…
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…
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…
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.
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…
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…
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…
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…
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…
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…