相关论文: Rational convex cones and cyclotomic multiple zeta…
In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…
We introduce adjoint cyclotomic multiple zeta values and cyclotomic multiple harmonic values. They are two variants of cyclotomic multiple zeta values, closely related to each other. They arise as key tools for the study of $p$-adic…
This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…
Multiple zeta values are real numbers defined by an infinite series generalizing values of the Riemann zeta function at positive integers. Finite truncations of this series are called multiple harmonic sums and are known to have interesting…
We study integrals over the triangle with vertices (1,0), (0,1), (1,1) that give linear combinations of multiple zeta values.
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…
We evaluate the multiple zeta values $\zeta(\{2\}^k)$ by proving a certain factorization property. The proof uses a combinatorial bijection and elementary telescoping series. We show how the infinite product for the sine function in fact…
The study of this paper is inspired by the conjecture of Zagier on the explicit dimension formula for the space of the same weight double zeta values in terms of the dimension of cusp forms for SL_{2}(Z). Our main result is to devise an…
We study logarithmic integrals of the form $\int_0^1 x^i\ln^n(x)\ln^m(1-x)dx$. They are expressed as a rational linear combination of certain rational numbers $(n,m)_i$, which we call tiered binomial coefficients, and products of the zeta…
We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…
We present a new "integral=series" type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear…
In this paper, we show that regularized elliptic multiple zeta values are given by polynomials in elliptic multiple zeta values with admissible indices and special ones whose indices consist of 0 and 1.
Ihara, Kaneko, and Zagier defined two regularizations of multiple zeta values and proved the regularization theorem that describes the relation between those regularizations. We show that the regularization theorem can be generalized to…
Enumerating integral orbits in prehomogeneous vector spaces plays an important role in arithmetic statistics. We describe a method of proving subconvexity of the zeta function enumerating the integral orbits, illustrated by proving a…
In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…
Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…
We study the values taken by the Riemann zeta-function $\zeta$ on discrete sets. We show that infinite vertical arithmetic progressions are uniquely determined by the values of $\zeta$ taken on this set. Moreover, we prove a joint discrete…
We provide a proof of a conjecture by Zhao concerning the structure of certain relations among cyclotomic multiple zeta values in weight two. We formulate this conjecture in a broader algebraic setting in which we give a natural equivalence…
Recently, the author defined multiple Dedekind zeta values [5] associated to a number K field and a cone C. These objects are number theoretic analogues of multiple zeta values. In this paper we prove that every multiple Dedekind zeta value…
Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values (MVZs) around 2016. In this paper, we will first establish some explicit formulas involving these values and their alternating version by using iterated integrals,…