Polylogarithms pdf
http://people.mpim-bonn.mpg.de/stavros/publications/resurgencepolylogarithms.pdf WebMar 1, 2011 · PDF In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. ... Keywords: polylogarithms; zeta functions; ...
Polylogarithms pdf
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WebFeb 11, 2024 · Download PDF Abstract: For an integer n>2 we define a polylogarithm, which is a holomorphic function on the universal abelian cover of C-{0,1} defined modulo (2 pi i)^n/(n-1)!. We use the formal properties of its functional relations to define groups lifting Goncharov's Bloch groups of a field F, and show that they fit into a complex lifting … WebElliptic polylogarithms are multi-valued analytic functions on a punctured ellip-tic curve. We realize the elliptic curve as the quotient of C by lattice L= Z˝ Z. Hence these functions can be described as functions on CnZ˝ Z 3. De nition 1.2 Elliptic …
WebMar 24, 2024 · Nielsen Generalized Polylogarithm. Download Wolfram Notebook. A generalization of the polylogarithm function defined by. The function reduces to the usual … WebAbstract. The fractional polylogarithms, depending on a complex parameter α, are defined by a series which is analytic inside the unit disk. After an elementary conversion of the series into an integral presen-tation, we show that the fractional polylogarithms are multivalued analytic functions in the complex plane minus 0 and 1.
Weband m. When x D0, our result implies the linear independence of polylogarithms of distinct algebraic numbers of arbitrary degree, subject to a metric condition. We give an outline of our proof together with concrete examples of linearly independent polylogarithms. 1. Introduction Let s be a nonnegative integer and 0 x <1 be a rational number. Webdescribe the scattering of elementary particles, polylogarithms are ubiquitous. One way to understand the connection between polylogarithms and Feynman integrals is through the …
Web, when s 1, … , s k are positive integers and z a complex number in the unit disk. For k = 1, this is the classical polylogarithm Li s (z).These multiple polylogarithms can be defined also in …
WebApr 4, 2024 · A bstract Elliptic multiple polylogarithms occur in Feynman integrals and in particular in scattering amplitudes. They can be characterized by their symbol, a tensor product in the so-called ... sharps lawn mower repairWebp-ADIC POLYLOGARITHMS 3 Choose a lifting of the absolute Frobenius of (X;M) ›OK k to (X;M) which is equivalent to giving a lifting FX: X ! X of the absolute Frobenius of X ›O K k such that FX(ti) = t p i ¢(unit) for each i such that ti is not invertible. We denote by ’ the endomorphism of A induced by FX. Giving a filtered convergent F-isocrystal on (X;M) is … sharps liquor store tazewell tnWebMar 8, 2007 · Download PDF Abstract: We investigate the elliptic analogs of multi-indexed polylogarithms that appear in the theory of the fundamental group of the projective line minus three points as sections of a universal nilpotent bundle with regular singular connection. We use an analytic uniformisation to derive the fundamental nilpotent De … sharps lever actionsharps locksmithingWebCluster polylogarithms on the configuration space 18 3.1. Quadrangular polylogarithms 18 3.2. The space of quadrangular polylogarithms 21 3.3. Proof of Theorems 1.1 22 3.4. sharp slides armyWebKey words: Polylogarithms, modular forms. Introduction The notion of the elliptic polylogarithm functions as a natural generalization of the usual polylogarithms was … sharp slimline dishwashers ukWebThe Computation of Polylogarithms David C. Wood ABSTRACT The polylogarithm function, Li p(z), is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter p and complex argument z. These are sufficient to evaluate it numerically, with reasonable efficiency, in all cases. 1. Definition sharp slimline integrated dishwasher