23 citations · 35 across the 50 of their papers we have counts for
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A modular relation involving a generalized digamma function and asymptotics of some integrals containing
Atul Dixit, Rahul Kumar
A modular relation of the form , where and , is obtained. It involves the generalized digamma function which was recently studied by…
Applications of Lipschitz summation formula and a generalization of Raabe's cosine transform
Atul Dixit, Rahul Kumar
General summation formulas have been proved to be very useful in analysis, number theory and other branches of mathematics. The Lipschitz summation formula is one of them. In this…
A finite analogue of a -series identity of Bhoria, Eyyunni and Maji and its applications
Atul Dixit, Khushbu Patel
Bhoria, Eyyunni and Maji recently obtained a four-parameter -series identity which gives as special cases not only all five entries of Ramanujan on pages 354 and 355 of his seco…
A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis
Atul Dixit, Shivajee Gupta, Akshaa Vatwani
We give a number field analogue of a result of Ramanujan, Hardy and Littlewood, thereby obtaining a modular relation involving the non-trivial zeros of the Dedekind zeta function.…
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…
Two General Series Identities Involving Modified Bessel Functions and a Class of Arithmetical Functions
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
We consider two sequences and , , generated by Dirichlet series $$\sum_{n=1}^{\infty}\frac{a(n)}{λ_n^{s}}\qquad\text{and}\qquad \sum_{n=1}^{\infty}\fra…