Atul Dixit

activity

20092026

most citedGeneralized Lambert series and arithmetic nature of odd zeta values

23 citations · 35 across the 50 of their papers we have counts for

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Showing 2023Show all

5 papers · 1 filter

math.NT2023

Recent developments pertaining to Ramanujan's formula for odd zeta values

Atul Dixit

In this expository article, we discuss the contributions made by several mathematicians with regard to a famous formula of Ramanujan for odd zeta values. The goal is to complement…

math.NT2023

Modular relations involving generalized digamma functions

Atul Dixit, Sumukha Sathyanarayana, N. Guru Sharan

Generalized digamma functions $ψ_{k} (x)$ , studied by Ramanujan, Deninger, Dilcher, Kanemitsu, Ishibashi etc., appear as the Laurent series coefficients of the zeta function associate…

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.NT2023

Modified Bessel Functions in Analytic Number Theory

Bruce C. Berndt, Atul Dixit, Rajat Gupta +1

The modified Bessel functions $K_{ν} (z)$ , or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic ident…

math.NT2023

Voronoi summation formula for the generalized divisor function $σ_{z}^{(k)} (n)$

Atul Dixit, Bibekananda Maji, Akshaa Vatwani

For a fixed $z \in C$ and a fixed $k \in N$ , let $σ_{z}^{(k)} (n)$ denote the sum of $z$ -th powers of those divisors $d$ of $n$ whose $k$ -th powers also divide $n$ . Th…

Recent developments pertaining to Ramanujan's formula for odd zeta values

Modular relations involving generalized digamma functions

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

Modified Bessel Functions in Analytic Number Theory

Voronoi summation formula for the generalized divisor function σz(k)​(n)

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

Voronoi summation formula for the generalized divisor function $σ_{z}^{(k)} (n)$