Related papers: Joint universality for Lerch zeta-functions

We evaluate certain multidimensional integrals in terms of the Lerch transcendent function $\Phi$, generalizing Guillera-Sondow's formulas. As an application, we get new representations of classical constants like Euler's constant $\gamma$…

Explicit bounds on the tails of the zeta function $\zeta$ are needed for applications, notably for integrals involving $\zeta$ on vertical lines or other paths going to infinity. Here we bound weighted $L^2$ norms of tails of $\zeta$. Two…

In this paper, we construct generalized $L$-functions associated to meromorphic modular forms of weight $\frac12$ for the theta group with a single simple pole in the fundamental domain. We then consider their behaviour towards $i\infty$…

Let $f_{\bf c}(r)=\sum_{n=0}^\infty e^{c_n}r^n$ be an analytic function; ${\bf c}=(c_n)\in l_\infty$. We assume that $r$ is some logarithmically convex and lower semicontinuous functional on a locally convex topological space $L$. In this…

The study of the Mittag-Leffler function and its various generalizations has become a very popular topic in mathematics and its applications. In the present paper we prove the following estimate for the $q$-Mittag-Leffler function:…

Let $q\ge3$ be an integer, $\chi$ denote a Dirichlet character modulo $q$, for any real number $a\ge 0$, we define the generalized Dirichlet $L$-functions $$ L(s,\chi,a)=\sum_{n=1}^{\infty}\frac{\chi(n)}{(n+a)^s}, $$ where $s=\sigma+it$…

For Hurwitz Zeta function,we consider its Taylor series expansion about various points as an analytic function of second variable in appropriate discs.We show that these Taylor are all polynomials in second variable for a non positive…

This is a conitunation of [1] and [2]. We prove that if function $f$ belongs to the class $\Lambda_{\omega} \overset{\text{def}}{=} \{f: \omega_{f}(\delta)\leq \text{const} \omega(\delta)\} $ for an arbitrary modulus of continuity $\omega$,…

An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.

The secondary zeta function is defined as a generalized zeta series over the imaginary parts of non-trivial zeros assuming (RH). This function admits Laurent series expansion at the double pole at $s=1$. In this article, we derive a new…

We establish the universality theorem for the first four symmetric power L-functions of automorphic forms and their associated Rankin-Selberg L-functions. This generalizes some results of Laurincikas & Matsumoto and Matsumoto respectively.

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

We give a new type of mixed discrete joint universality properties, which is satisfied by a wide class of zeta-functions. We study the universality for a certain modification of a Matsumoto zeta-function and a periodic Hurwitz zeta-function…

Let $q\ge3$ be an integer, $\chi$ denote a Dirichlet character modulo $q$, for any real number $a\ge 0$, we define the generalized Dirichlet $L$-functions $$ L(s,\chi,a)=\sum_{n=1}^{\infty}\frac{\chi(n)}{(n+a)^s}, $$ where $s=\sigma+it$…

We define generalised zeta functions associated to indefinite quadratic forms of signature (g-1,1) -- and more generally, to complex symmetric matrices whose imaginary part has signature (g-1,1) -- and we investigate their properties. These…

Let $\mathcal S$ denote the class of all functions of the form $f(z)=z+a_2z^2+a_3z^3+\cdots$ which are analytic and univalent in the open unit disk $\ID$ and, for $\lambda >0$, let $\Phi_\lambda (n,f)=\lambda a_n^2-a_{2n-1}$ denote the…

For an arbitrary complex number $a\neq 0$ we consider the distribution of values of the Riemann zeta-function $\zeta$ at the $a$-points of the function $\Delta$ which appears in the functional equation $\zeta(s)=\Delta(s)\zeta(1-s)$. These…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

Let ${\mathcal A}$ be the class of functions analytic in the unit disk ${\mathbb D} := \{ z\in {\mathbb C}:\, |z| < 1 \}$ and normalized such that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we study the class $\mathcal{U}(\lambda)$,…

It is known that the Selberg zeta function for the modular group has an expression in terms of the class numbers and the fundamental units of the indefinite binary quadratic forms. In the present paper, we generalize such a expression to…