Abstract We study wide moments of Dirichlet L-functions using analytic properties the Lerch zeta function. Among other things we obtain an asymptotic expansion (with arbitrary twists) extending results Heath-Brown. also give applications to non-vanishing.

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by second author. Applying Mellin transformation to function, define new class zeta type functions, which is related interpolation functions Apostol–Bernoulli polynomials, Bernoulli Euler polynomials. This Hurwitz alternating Lerch function. Furthermore, using these derive ...

In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...

For a given rational number $x$ and an integer $s\geq 1$, consider generalized polylogarithmic function, often called the Lerch defined by $$\Phi _{s}(x,z)= \sum _{k=0}^{\infty }\frac{z^{k+1}}{(k+x+1)^s}.$$ We prove linear independence

ABSTRACT In the present paper we evaluate a general integral involving the product of the extension of the Hurwitz-Lerch Zeta function, product of two ,Bessel functions, multivariable Aleph-function Jacobi polynomial, the multivariable I-function defined by Prasad [4] and general class of polynomials of several variables. The importance of the result established in this paper lies in the fact t...