23 citations · 35 across the 50 of their papers we have counts for
4 papers · 2 filters
Zeros of combinations of the Riemann -function and the confluent hypergeometric function on bounded vertical shifts
Atul Dixit, Rahul Kumar, Bibekananda Maji +1
In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Re…
Generalized Lambert series and arithmetic nature of odd zeta values
Atul Dixit, Bibekananda Maji
It is pointed out that the generalized Lambert series studied by Kanemitsu, Tanigawa and Yoshimoto can be found on p…
A generalized modified Bessel function and a higher level analogue of the theta transformation formula
Atul Dixit, Aashita Kesarwani, Victor H. Moll +1
A new generalization of the modified Bessel function of the second kind is studied. Elegant series and integral representations, a differential-difference equation and a…
Sums of squares and products of Bessel functions
Bruce C. Berndt, Atul Dixit, Sun Kim +1
Let denote the number of representations of the positive integer as the sum of squares. We rigorously prove for the first time a Voronoi summation formula for $r_k…