Zobrazeno 1 - 10
of 5 222
pro vyhledávání: '"polylogarithm"'
Autor:
Mishra, Deepshikha, Swaminathan, A.
This paper focuses on the generalized polylogarithm $\Phi_{p, q}(a, b; z)$, which extends the notion of classical polylogarithm. A new integral representation for $\Phi_{p, q}(a, b; z)$ is derived. Using this integral representation, we discuss its c
Externí odkaz:
http://arxiv.org/abs/2412.08552
Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and provide two
Externí odkaz:
http://arxiv.org/abs/2404.15210
Akademický článek
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Publikováno v:
Applicable Analysis and Discrete Mathematics, 2023 Apr 01. 17(1), 25-46.
Externí odkaz:
https://www.jstor.org/stable/27281393
Autor:
Dupont, Clément, Fresán, Javier
Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial variation.
Externí odkaz:
http://arxiv.org/abs/2305.00789
Publikováno v:
Applied Mathematics in Science & Engineering. Dec2023, Vol. 31 Issue 1, p1-14. 14p.
Publikováno v:
Mathematics of Computation, 2018 Mar 01. 87(310), 855-877.
Externí odkaz:
https://www.jstor.org/stable/90016861
Autor:
Hopper, Eric
Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over $\mathbb{Z}[\mu_N,1/N]$. Brown and Hain--Matsumoto computed the depth 2 quadratic relations of the motivic Galois group of this category for $N = 1$.
Externí odkaz:
http://arxiv.org/abs/2208.01153
The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields
Autor:
Bannai, Kenichi, Bekki, Hohto, Hagihara, Kei, Ohshita, Tatsuya, Yamada, Kazuki, Yamamoto, Shuji
Publikováno v:
Advances in Mathematics 448 (2024) 109716
In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylog
Externí odkaz:
http://arxiv.org/abs/2207.03285
Autor:
Au, Kam Cheong
We give systematic method that can convert many values of multiple polylogarithm at algebraic arguments into colored multiple zeta values (CMZV). Moreover, a new method to generate nonstandard relations of CMZVs is discovered. Some applications to po
Externí odkaz:
http://arxiv.org/abs/2201.01676