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Related papers: Trivial multiple zeta values in Tate algebras

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

Number Theory · Mathematics 2007-05-23 Sergey Zlobin

We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including the field of algebraic numbers and the algebraic closure of a finite field, we arrive at a complete description…

Algebraic Geometry · Mathematics 2019-09-18 Martin Gallauer

We study a family of mixed Tate motives over $\mathbb{Z}$ whose periods are linear forms in the zeta values $\zeta(n)$. They naturally include the Beukers-Rhin-Viola integrals for $\zeta(2)$ and the Ball-Rivoal linear forms in odd zeta…

Algebraic Geometry · Mathematics 2019-02-20 Clément Dupont

This paper is a culmination of [CM20] on the study of multiple zeta values (MZV's) over function fields in positive characteristic. For any finite place $v$ of the rational function field $k$ over a finite field, we prove that the $v$-adic…

Number Theory · Mathematics 2020-07-17 Chieh-Yu Chang , Yen-Tsung Chen , Yoshinori Mishiba

In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…

Combinatorics · Mathematics 2022-02-04 Markus Kuba

We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of "decalage" that avoids using an integral representation of…

Number Theory · Mathematics 2007-05-23 Marc De Crisenoy , Driss Essouabri

Multiple zeta values (MZVs) with certain repeated arguments or certain sums of cyclically generated MZVs are evaluated as rational multiple of powers of $\pi^2$. In this paper, we give a short and simple proof of the remarkable evaluations…

Number Theory · Mathematics 2008-03-03 Shuichi Muneta

In this paper, we introduce multiple zeta dagger values and special values of Carlitz multiple dagger polylogarithms, and study their properties. In particular, using these values, we construct a non-trivial involution on a certain quotient…

Number Theory · Mathematics 2026-01-05 Yoshinori Mishiba

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…

Number Theory · Mathematics 2011-03-11 Shingo Saito , Tatsushi Tanaka , Noriko Wakabayashi

We show that trivial extensions of gentle tree algebras are exactly Brauer tree algebras without exceptional vertex. We also give a characterization for the algebras whose trivial extensions are Brauer line/star/cycle algebras. As a…

Representation Theory · Mathematics 2025-03-14 Qi Wang , Yingying Zhang

Multiple modular values are a common generalisation of multiple zeta values and periods of modular forms, and are periods of a hypothetical Tannakian category of mixed modular motives. They are given by regularised iterated integrals on the…

Number Theory · Mathematics 2017-06-20 Francis Brown

We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…

Number Theory · Mathematics 2023-08-22 Henrik Bachmann , Jan-Willem van Ittersum

Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present paper we establish an effective criterion for Eulerian multizeta values, which…

Number Theory · Mathematics 2020-07-09 Chieh-Yu Chang , Matthew A. Papanikolas , Jing Yu

In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between…

Number Theory · Mathematics 2011-08-25 José Alejandro Lara Rodríguez

We study (support) $\tau$-tilting modules over the trivial extensions of finite dimensional algebras. More precisely, we construct two classes of (support)$\tau$-tilting modules in terms of the adjoint functors which extend and generalize…

Representation Theory · Mathematics 2022-02-21 Zhi-Wei Li , Xiaojin Zhang

The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed…

Number Theory · Mathematics 2014-06-11 Shingo Saito , Noriko Wakabayashi

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum…

Number Theory · Mathematics 2013-03-12 Tomoya Machide

We present several conjectures on multiple q-zeta values and on the role they play in certain problems of enumerative geometry.

Algebraic Geometry · Mathematics 2014-04-16 Andrei Okounkov

In this paper, we study transcendence theory for Thakur multizeta values in positive characteristic. We prove an analogue of the strong form of Goncharov's conjecture. We also establish the same result for Carlitz multiple polylogarithms at…

Number Theory · Mathematics 2019-02-20 Chieh-Yu Chang

In 2022, Gezmis and Pellarin introduced and studied the concept of trivial multiple zeta values, along with a map from the vector space spanned by these values to the vector space spanned by Thakur's multiple zeta values. Their construction…

Number Theory · Mathematics 2023-06-23 Khac Nhuan Le , Kien Huu Nguyen