Related papers: Multiple Rogers--Ramanujan type identities for tor…

We provide a formula for the generating series of the zeta function $Z(X,t)$ of symmetric powers $Sym^n X$ of varieties over finite fields. This realizes $Z(X,t)$ as an exponentiable motivic measure whose associated Kapranov motivic zeta…

In this paper, we derive a unified generalization of Ramanujan's transformation identities for the theta function $f(a,b)$, originally appearing in Ramanujan's Notebooks, Parts~III and IV. Using an approach based on residue-class…

Partitions associated with mock theta functions have received a great deal of attention in the literature. Recently, Choi and Kim derived several partition identities from the third and sixth order mock theta functions. In addition, three…

We prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular,…

In this paper, we consstruct a new extended q-Bernoulli numbers and poly nomials. From these numbers, we derive the multiple zeta functions and give some relations between multiple Bernoulli numbers and multiple zeta functions.

In recent years, there has been intensive research on the ${\mathbb Q}$-linear relations between multiple zeta (star) values. In this paper, we prove many families of identities involving the $q$-analog of these values, from which we can…

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…

Ramanujan presented four identities for third order mock theta functions in his Lost Notebook. In 2005, with the aid of complex analysis, Yesilyurt first proved these four identities. Recently, Andrews et al. provided different proofs by…

In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among…

We present some applications of the Kudla-Millson and the Millson theta lift. The two lifts map weakly holomorphic modular functions to vector valued harmonic Maass forms of weight $3/2$ and $1/2$, respectively. We give finite algebraic…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

The Kronecker theta function is a quotient of the Jacobi theta functions, which is also a special case of Ramanujan's $_1\psi_1$ summation. Using the Kronecker theta function as building blocks, we prove a decomposition theorem for theta…

In this paper, we give some extensions for Ramanujan's circular summation formula with the mixed products of two Jacobi's theta functions. As some applications, we also obtain many interesting identities of Jacobi's theta functions.

Let $\zeta(.)$ denote the Riemann zeta function and let $a(.)$ and $A(.)$ respectively denote a multiplicative function and its corresponding summatory function. We consider the correlation $$ \langle a(n)A(n-1) \rangle (T) =…

We consider the series $\sum_{n=1}^{\infty} z^{n} (a_{n} + x)^{-s}$ where $a_{n}$ satisfies a linear recurrence of arbitrary degree with integer coefficients. Under appropriate conditions, we prove that it can be continued to a meromorphic…

Polynomial generalizations of all 130 of the identities in Slater's list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial…

We present here a way to evaluate a very wide class of integrals relating Ramanujans continued fraction and q-product. To do this we explore briefily a differential equation, which relates these two functions

The main aim of this paper is to investigate and introduce relations between the numbers of k-ary Lyndon words and unified zeta-type functions which was defined by Ozden et al [15, p. 2785]. Finally, we give some identities on generating…

Formulas for the topological zeta functions of suspensions by 2 points are due to Artal et al. We generalize these formulas to the motivic level and for arbitrary suspensions, by using a stratification principle and classical techniques of…

Lin and Wang defined a model of random walks on knot diagrams and interprete the Alexnader polynomials and the colored Jones polynomials as Ihara zeta functions, i.e. zeta functions defined by counting cycles on the knot diagram. Using this…