Sums of Zeros for Certain Special Functions

TL;DR

This paper investigates the sums of zeros of special functions like q-Airy, q-Bessel, Bessel, Airy, Riemann zeta, and Dirichlet L-series, providing insights into their zero distributions.

Contribution

It offers new analytical results on the sums of zeros for various special functions, extending classical zero sum formulas to q-analogues and other functions.

Findings

Derived explicit formulas for sums of zeros of q-Airy and q-Bessel functions

Established relationships between zeros of classical and q-analog special functions

Provided insights into the zero distribution of the Riemann zeta and Dirichlet L-series

Abstract

Key words and phrases: q-Airy function (Ramanujan's entire function); q-Bessel function; Bessel function; Airy function; Riemann zeta function; Dirichlet L-series.