108 citations · 307 across the 89 of their papers we have counts for
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Ramanujan and Koshliakov Meet Abel and Plana
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
The neglected Russian mathematician, N.~S.~Koshliakov, derived beautiful generalizations of the classical Abel--Plana summation formula through a setting arising from a boundary va…
A Class of Identities Associated with Dirichlet Series Satisfying Hecke's Functional Equation
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
We consider two sequences and , , generated by Dirichlet series of the forms $$\sum_{n=1}^{\infty}\frac{a(n)}{λ_n^{s}}\qquad\text{and}\qquad \sum_{n=1}…
On -adic uniformization of abelian varieties with good reduction
Adrian Iovita, Jackson S. Morrow, Alexandru Zaharescu
Let be a rational prime, let denote a finite, unramified extension of , the maximal unramified extension of , some fixed alge…
Two-parameter Identities for Divisor Sums in Algebraic Number Fields
Bruce C. Berndt, Martino Fassina, Sun Kim +1
In a one-page fragment published with his lost notebook, Ramanujan stated two double series identities associated, respectively, with the famous Gauss Circle and Dirichlet Divisor…
Energy bounds for modular roots and their applications
Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski +1
We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebra…
A zero density estimate and fractional imaginary parts of zeros for -functions
Olivia Beckwith, Di Liu, Jesse Thorner +1
We prove an analogue of Selberg's zero density estimate for that holds for any -function. We use this estimate to study the distribution of the vector of…