نتایج جستجو برای: Polylogarithm functions

تعداد نتایج: 490764  

Journal: :Tatra mountains mathematical publications 2023

Abstract We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well its connection to hypergeometric series.

2005
Guido Kings

The degeneration of the polylogarithm on the universal abelian scheme over a Hilbert modular variety at the boundary is described in terms of (critical) special values of the L-function of the totally real field defining the variety. This gives a relation between the polylogarithm on abelian schemes and special values of L-functions. 2000 Mathematics Subject Classification: 11F41, 11G55, 11R42

2006
Charles L. Epstein Jack Morava

converges when |z| < 1, defining the classical polylogarithm function, equal to − log(1 − z) when s = 1. In general, the behavior of these functions at z = 1 is complicated: it is known, for example, that Lis has an analytic continuation to the cut plane C − 1,∞). The fact that the ‘modified’ polylogarithm of Bloch, Ramakrishnan, Wigner, Wojtkowiak, Zagier, . . . , defined as the real, or imagi...

2008
DIRK KREIMER

We discuss in an introductory manner structural similarities between the polylogarithm and Green functions in quantum field theory.

2008
Steven J. Miller

We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to expanding moments of Satake parameters of holomorphic cuspidal newforms in terms of the moments of the corresponding Fourier coefficients, which has applications i...

2008
Toufik Mansour

We present several identities for sums of q-polylogarithm functions. Our motivation for these are the relations between the q-zeta function (see [3, 4, 12] and references therein), q-polylogarithm functions (see below) and the quantum group SUq(2). More precisely, the left regular representation of the quantum group SUq(2) is the coordinate ring A(SUq(2)) represented as a left Uq(sl(2))-module....

2008
KENICHI BANNAI SHINICHI KOBAYASHI

In this paper, we construct p-adic analogues of the Kronecker double series, which we call the Eisenstein-Kronecker series, as Coleman functions on an elliptic curve with complex multiplication. We then show that the periods of the specialization of the p-adic elliptic polylogarithm sheaf to arbitrary non-zero points of the elliptic curve may be expressed using these functions.

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