3 citations · 9 across the 18 of their papers we have counts for
21 papers
Modified Bessel Functions in Analytic Number Theory
Bruce C. Berndt, Atul Dixit, Rajat Gupta +1
The modified Bessel functions , or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic ident…
Proofs of McIntosh's Conjecture on Franel Integrals and Two Generalizations
Bruce C. Berndt, Likun Xie, Alexandru Zaharescu
We provide a proof of a conjecture made by Richard McIntosh in 1996 on the values of the Franel integrals, where is the first peri…
Finite trigonometric sums arising from Ramanujan's theta functions
Bruce C. Berndt, Sun Kim, Alexandru Zaharescu
Two classes of finite trigonometric sums, each involving only 's, are evaluated in closed form. The previous and original proofs arise from Ramanujan's theta functions and mo…
Exact evaluations and reciprocity theorems for finite trigonometric sums
Bruce C. Berndt, Sun Kim, Alexandru Zaharescu
We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour…
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…
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…