scholarly journals INTERPOLATED SCHUR MULTIPLE ZETA VALUES

2017 ◽  
Vol 104 (3) ◽  
pp. 289-307 ◽  
Author(s):  
HENRIK BACHMANN
Keyword(s):  
Recent Work ◽  
Analogous Result ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

Inspired by the recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki, we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will be a Jacobi–Trudi formula for a certain class of these new objects. This generalizes an analogous result for Schur multiple zeta values and implies algebraic relations between interpolated multiple zeta values.

ON A GENERALISATION OF A RESTRICTED SUM FORMULA FOR MULTIPLE ZETA VALUES AND FINITE MULTIPLE ZETA VALUES

2019 ◽  
Vol 101 (1) ◽  
pp. 23-34
Author(s):  
HIDEKI MURAHARA ◽  
TAKUYA MURAKAMI
Keyword(s):  
Linear Relation ◽  
Analogous Result ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Natural Generalisation ◽  
Sum Formula

We prove a new linear relation for multiple zeta values. This is a natural generalisation of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.

scholarly journals THE STRONG CHOWLA–MILNOR SPACES AND A CONJECTURE OF GUN, MURTY AND RATH

2012 ◽  
Vol 08 (05) ◽  
pp. 1301-1314
Author(s):  
TAPAS CHATTERJEE
Keyword(s):  
Lower Bound ◽  
Recent Work ◽  
Number Field ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Positive Integers

In a recent work, Gun, Murty and Rath formulated the Strong Chowla–Milnor conjecture and defined the Strong Chowla–Milnor space. In this paper, we proved a non-trivial lower bound for the dimension of these spaces. We also obtained a conditional improvement of this lower bound and noted that an unconditional improvement of this lower bound will lead to irrationality of both ζ(k) and ζ(k)/πk for all odd positive integers k. Following Gun, Murty and Rath, we define generalized Zagier spaces Vp(K) for multiple zeta values over a number field K. We prove that the dimension of V4d+2(K) for d ≥ 1, is at least 2, assuming a conjecture of Gun, Murty and Rath.

Motivic multiple zeta values relative to μ2

2020 ◽  
Vol 14 (10) ◽  
pp. 2685-2712
Author(s):  
Zhongyu Jin ◽  
Jiangtao Li
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals ON MULTIPLE ZETA VALUES OF EXTREMAL HEIGHT

2015 ◽  
Vol 93 (2) ◽  
pp. 186-193 ◽  
Author(s):  
MASANOBU KANEKO ◽  
MIKA SAKATA
Keyword(s):  
Explicit Formula ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values ◽  
Sum Formula

We give three identities involving multiple zeta values of height one and of maximal height: an explicit formula for the height-one multiple zeta values, a regularised sum formula and a sum formula for the multiple zeta values of maximal height.

scholarly journals Truncated t-adic symmetric multiple zeta values and double shuffle relations

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Masataka Ono ◽  
Shin-ichiro Seki ◽  
Shuji Yamamoto
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals On multiple zeta values and finite multiple zeta values of maximal height

2018 ◽  
Vol 14 (04) ◽  
pp. 975-987
Author(s):  
Hideki Murahara ◽  
Mika Sakata
Keyword(s):  
Explicit Formula ◽  
Alternative Proof ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Maximal Height ◽  
Zeta Values

An explicit formula for the height-one multiple zeta values (MZVs) was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values (FMZVs).

scholarly journals Nested Sums of Symbols and Renormalized Multiple Zeta Values

2010 ◽  
Vol 2010 (24) ◽  
pp. 4628-4697 ◽  
Author(s):  
Dominique Manchon ◽  
Sylvie Paycha
Keyword(s):  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values
Sign in / Sign up

Export Citation Format

Share Document