  Recently, Dixit et al. established a very elegant generalization of Hardy's
Theorem concerning the infinitude of zeros that the Riemann zeta function
possesses at its critical line. By introducing a general transformation formula
for the theta function involving the Bessel and Modified Bessel functions of
the first kind, we extend their result to a class of Dirichlet series
satisfying Hecke's functional equation. In the process, we also find new
generalizations of classical identities in Analytic number theory.
