We study topics related to zeros of Dirichlet series and entire functions. A large part of the thesis is devoted to the location of zeros of Dirichlet series via density criteria. We establish the Nyman-Beruling criterion for a wide class of Dirichlet series and the Báez-Duarte criterion for Dirichlet L-functions in the semi-plane R(s)>1/p, for p ∈...
We study topics related to zeros of Dirichlet series and entire functions. A large part of the thesis is devoted to the location of zeros of Dirichlet series via density criteria. We establish the Nyman-Beruling criterion for a wide class of Dirichlet series and the Báez-Duarte criterion for Dirichlet L-functions in the semi-plane R(s)>1/p, for p ∈...
We study topics related to zeros of Dirichlet series and entire functions. A large part of the thesis is devoted to the location of zeros of Dirichlet series via density criteria. We establish the Nyman-Beruling criterion for a wide class of Dirichlet series and the Báez-Duarte criterion for Dirichlet L-functions in the semi-plane R(s)>1/p, for p ∈...
Published in Mathematical Notes
A limit theorem involving an increasing modulus of the character is obtained for twists with the Dirichlet character of L-functions of elliptic curves.
We establish lower bounds for (i) the numbers of positive and negative terms and (ii) the number of sign changes in the sequence of Fourier coefficients at squarefree integers of a half-integral weight modular Hecke eigenform.
Published in Integral Equations and Operator Theory
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as the kernel function. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy space is shown through the Bose–Einstein integral equation. Next we consider function theoretic operators ove...
Published in Mathematical Notes
We obtain asymptotic formulas for the mean values of a number of arithmetic functions f = f(n) on a “short” interval of the form x
This article proves q-analogues of classical results for Ehrhart polynomials of Gorensteinpolytopes, in the general setting of q-Ehrhart polynomials of lattice polytopes. We then study thevalues on these polynomials of a specific linear form (involving Carlitz’ q-analogues of Bernoullinumbers). We also introduce a zeta function associated to an Ehr...
This article considers some q-analogues of classical results concerning the Ehrhart polynomials of Gorenstein polytopes, namely properties of their q-Ehrhart polynomial with respect to a good linear form. Another theme is a specific linear form Ψ (involving Carlitz' q-analogues of Bernoulli numbers) on the space of polynomials, for which one shows ...
Published in Indian Journal of Pure and Applied Mathematics
We study the lacunary Dirichlet series obtained from the reciprocals of sth powers of balancing numbers. This function admits an analytic continuation to the entire complex plane. The series converges to irrational numbers at odd negative integral arguments. Finally, we also study the analytic continuation of the balancing L-function.
