Zobrazeno 1 - 10
of 19
pro vyhledávání: '"11M32, 11F11"'
Autor:
Bachmann, Henrik
Multiple Eisenstein series are holomorphic functions in the complex upper-half plane, which can be seen as a crossbreed between multiple zeta values and classical Eisenstein series. They were originally defined by Gangl-Kaneko-Zagier in 2006, and sin
Externí odkaz:
http://arxiv.org/abs/2212.10700
Autor:
Bachmann, Henrik, Burmester, Annika
We construct a family of $q$-series with rational coefficients satisfying a variant of the extended double shuffle equations, which are a lift of a given $\mathbb{Q}$-valued solution of the extended double shuffle equations. These $q$-series will be
Externí odkaz:
http://arxiv.org/abs/2203.17074
We introduce the formal double Eisenstein space $\mathcal{E}_k$, which is a generalization of the formal double zeta space $\mathcal{D}_k$ of Gangl-Kaneko-Zagier, and prove analogues of the sum formula and parity result for formal double Eisenstein s
Externí odkaz:
http://arxiv.org/abs/2109.04267
Autor:
Bachmann, Henrik
In this survey article, we discuss the algebraic structure of q-analogues of multiple zeta values, which are closely related to derivatives of Eisenstein series. Moreover, we introduce the formal double Eisenstein space, which generalizes the formal
Externí odkaz:
http://arxiv.org/abs/2108.08634
Autor:
Bachmann, Henrik
This work is an example driven overview article of recent works on the connection of multiple zeta values, modular forms and q-analogues of multiple zeta values given by multiple Eisenstein series.
Comment: 66 pages
Comment: 66 pages
Externí odkaz:
http://arxiv.org/abs/1704.06930
Autor:
Bachmann, Henrik
We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the derivative
Externí odkaz:
http://arxiv.org/abs/1609.09182
Autor:
Bachmann, Henrik
We study the algebra of certain $q$-series, called bi-brackets, whose coefficients are given by weighted sums over partitions. These series incorporate the theory of modular forms for the full modular group as well as the theory of multiple zeta valu
Externí odkaz:
http://arxiv.org/abs/1504.08138
Autor:
Bachmann, Henrik, Tasaka, Koji
We study the multiple Eisenstein series introduced by Gangl, Kaneko and Zagier. We give a proof of (restricted) finite double shuffle relations for multiple Eisenstein series by developing an explicit connection between the Fourier expansion of multi
Externí odkaz:
http://arxiv.org/abs/1501.03408
Autor:
Kaneko, Masanobu, Tasaka, Koji
We study the double shuffle relations satisfied by the double zeta values of level 2, and introduce the double Eisenstein series of level 2 which satisfy the double shuffle relations. We connect the double Eisenstein series to modular forms of level
Externí odkaz:
http://arxiv.org/abs/1112.5697
Autor:
Koji Tasaka, Masanobu Kaneko
We study the double shuffle relations satisfied by the double zeta values of level 2, and introduce the double Eisenstein series of level 2 which satisfy the double shuffle relations. We connect the double Eisenstein series to modular forms of level
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c87cd3e90e8b5d41ad8c0ab8f339766a
http://arxiv.org/abs/1112.5697
http://arxiv.org/abs/1112.5697