Related papers: A continuous version of multiple zeta values with …

The zeta functions for the Schr\"odinger equation with a triangular potential are investigated. Values of the zeta functions are computed using both the Weierstrass factorization theorem and analytic continuation via contour integration.…

We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta…

In this paper, we introduce zeta values of rational convex cones, which is a generalization of cyclotomic multiple zeta values. These zeta values have integral expressions. The main theorem asserts that zeta values of cones can be expressed…

In this PhD thesis we study holomorphic and non-holomorphic elliptic analogues of multiple zeta values, namely elliptic multiple zeta values and modular graph functions. Both classes of functions have been discovered very recently, and are…

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.

This is an expository paper on the meromorphic continuation of zeta functions with Euler products (for example zeta functions of groups and height zeta functions) or without (for example the Goldbach zeta function). As an application we…

We establish the quaternionic weighted zeta function of a graph and its Study determinant expressions. For a graph with quaternionic weights on arcs, we define a zeta function by using an infinite product which is regarded as the Euler…

In this paper, we show that the cyclotomic symmetric multiple zeta values, independently proposed by Jarossay, Singar and Zhao, and Tasaka, span the space of the cyclotomic multiple zeta values modulo $\pi i$.

In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…

In this paper we show that the iterated integrals on products of one variable multiple polylogarithms from 0 to 1 are actually multiple zeta values if they are convergent. In the divergent case, we define regularized iterated integrals from…

We give an explicit representation for the sums of multiple zeta-star values of fixed weight and height in terms of Riemann zeta values.

We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\leq 2$ and the evaluation of…

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…

Finite Euler product is known to be one of the classical zeta functions in number theory. In [1], [2] and [3], we have introduced some multivariable zeta functions and studied their definable probability distributions on R^d. They include…

We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.

Let $A,B \subseteq \mathbb{R}^d $ both span $\mathbb{R}^d$ such that $\langle a, b \rangle \in \{0,1\}$ holds for all $a \in A$, $b \in B$. We show that $ |A| \cdot |B| \le (d+1) 2^d $. This allows us to settle a conjecture by Bohn, Faenza,…

We obtain two-variable Hecke-Rogers identities for three universal mock theta functions. This implies that many of Ramanujan's mock theta functions, including all the third order functions, have a Hecke-Rogers-type double sum…

The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper…

We prove two conjectures on the spaces generated by multiple $q$-zeta values. More precisely, we show that the spaces $Z_q^{\mathrm{o}}$ and $Z_{q,1}^{\mathrm{o}}$ already generate the larger spaces $Z_q$ and $Z_{q,1}$, respectively. Our…