scholarly journals Multiple Eisenstein Series and q-Analogues of Multiple Zeta Values

2020 ◽  
pp. 173-235
Author(s):  
Henrik Bachmann
Keyword(s):  
Eisenstein Series ◽  
Multiple Zeta Values ◽  
Multiple Zeta ◽  
Zeta Values

scholarly journals Multiple Dedekind zeta functions

2017 ◽  
Vol 2017 (722) ◽  
Author(s):  
Ivan Emilov Horozov
Keyword(s):  
Eisenstein Series ◽  
Zeta Functions ◽  
Quadratic Fields ◽  
Multiple Zeta Values ◽  
Imaginary Quadratic Fields ◽  
Iterated Integrals ◽  
Multiple Zeta ◽  
Zeta Values ◽  
New Type

AbstractIn this paper we define multiple Dedekind zeta values (MDZV), using a new type of iterated integrals, called iterated integrals on a membrane. One should consider MDZV as a number theoretic generalization of Euler’s multiple zeta values. Over imaginary quadratic fields MDZV capture, in particular, multiple Eisenstein series [

scholarly journals A CLASS OF NONHOLOMORPHIC MODULAR FORMS II: EQUIVARIANT ITERATED EISENSTEIN INTEGRALS

2020 ◽  
Vol 8 ◽  
Author(s):  
FRANCIS BROWN
Keyword(s):  
Eisenstein Series ◽  
Modular Forms ◽  
Multiple Zeta Values ◽  
New Family ◽  
Algebra Of Functions ◽  
Multiple Zeta ◽  
Zeta Values ◽  
Upper Half Plane ◽  
Real Analytic ◽  
Holomorphic Modular Forms

We introduce a new family of real-analytic modular forms on the upper-half plane. They are arguably the simplest class of ‘mixed’ versions of modular forms of level one and are constructed out of real and imaginary parts of iterated integrals of holomorphic Eisenstein series. They form an algebra of functions satisfying many properties analogous to classical holomorphic modular forms. In particular, they admit expansions in $q,\overline{q}$ and $\log |q|$ involving only rational numbers and single-valued multiple zeta values. The first nontrivial functions in this class are real-analytic Eisenstein series.

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
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