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A class of identities associated with Dirichlet series satisfying Hecke's functional equation

Berndt, Bruce C.; Dixit, Atul; Gupta, Rajat; Zaharescu, Alexandru (American Mathematical Society, 2022-06)

We consider two sequences a(n) and b(n), 1 ? n < ?, generated by Dirichlet series of the forms satisfying a familiar functional equation involving the gamma function ?(s). A general identity is established. Appearing on ...
Generalizations of the Andrews-Yee identities associated with the mock theta functions ω(q)and ν(q)

Berndt, Bruce C.; Dixit, Atul; Gupta, Rajat (Springer, 2021-10)

George Andrews and Ae Ja Yee recently established beautiful results involving bivariate generalizations of the third-order mock theta functions ω(q) and ν(q), thereby extending their earlier results with the second author. ...
On a theorem of A. I. Popov on sums of squares

Dixit, Atul; Kim, Sun; Zaharescu, Alexandru; Berndt, Bruce C. (American Mathematical Society, 2017)
Ramanujan's beautiful integrals

Berndt, Bruce C.; Dixit, Atul (Episciences, 2021-05)
Sums of squares and products of Bessel functions

Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru (Elsevier, 2018-11)

Letrk(n) denote the number of representations of the positive integernas thesum ofksquares. We rigorously prove for the first time a Vorono ?? summation formula forrk(n), k?2,proved incorrectly by A. I. Popov and later ...

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