Zobrazeno 1 - 10
of 7 143
pro vyhledávání: '"Polylogarithms"'
We define a Hopf algebra of polylogarithms of an infinite field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and mimics Goncharov's construction of higher Bloch groups. We also discus
Externí odkaz:
http://arxiv.org/abs/2411.15071
Autor:
Bolbachan, Vasily
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show tha
Externí odkaz:
http://arxiv.org/abs/2411.03889
Autor:
Kawamura, Hanamichi
There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them via iterated integrals and its symmetric counterpart by a similar meth
Externí odkaz:
http://arxiv.org/abs/2411.08711
Autor:
D'Hoker, Eric, Schlotterer, Oliver
A recent construction of polylogarithms on Riemann surfaces of arbitrary genus in arXiv:2306.08644 is based on a flat connection assembled from single-valued non-holomorphic integration kernels that depend on two points on the Riemann surface. In thi
Externí odkaz:
http://arxiv.org/abs/2407.11476
We study the asymptotic behavior of a multiple series of Mordell-Tornheim type and its integral analogue at x=0. Our approach is to show a relation between the multiple series and its integral analogue by using Abel's summation formula, and to deeply
Externí odkaz:
http://arxiv.org/abs/2409.19980
Autor:
Genčev, Marian
The objective of the paper is the study of Mneimneh-like sums with a parametric variant of the multiple harmonic-star values. We generalize and resolve the Pan-Xu conjecture on generalized Mneimneh-like sums and present their transformation. As an ap
Externí odkaz:
http://arxiv.org/abs/2408.16148
Elliptic polylogarithms can be defined as iterated integrals on a genus-one Riemann surface of a set of integration kernels whose generating series was already considered by Kronecker in the 19th century. In this article, we employ the Schottky param
Externí odkaz:
http://arxiv.org/abs/2406.10051
Unifying trigonometric and hyperbolic function derivatives via negative integer order polylogarithms
Autor:
Ducharme, Andrew
Special functions like the polygamma, Hurwitz zeta, and Lerch zeta functions have sporadically been connected with the nth derivatives of trigonometric functions. We show the polylogarithm $\text{Li}_s(z)$, a function of complex argument and order $z
Externí odkaz:
http://arxiv.org/abs/2405.19371