Polylogarithms pdf

Webple polylogarithms, the formal KZ equation and the Gauss hypergeometric equation. In Section 2, we consider the analytic continuation of the multiple polylogarithms of one variable to the universal covering space of P1−{0,1,∞} as an analytic function. In Section 3, we give an expression of the Gauss hypergeometric function WebMar 24, 2024 · Nielsen Generalized Polylogarithm. Download Wolfram Notebook. A generalization of the polylogarithm function defined by. The function reduces to the usual …

[PDF] Elliptic polylogarithms and iterated integrals on elliptic …

WebThe 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 Webobtain a representation of polylogarithms which will be single valued on the cut plane. For example, for the dilogarithm we obtain Li 2(z) = Z z 0 ln(1 u) u du for z2C (1;1): 6. The … dichotomies in all the pretty horses https://aeholycross.net

Polylogarithm - Wikipedia

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 … WebAug 24, 2024 · View PDF on arXiv. Save to Library Save. Create Alert Alert. Cite. Share This Paper. 2 Citations. Background Citations. 2. View All. 2 Citations. Citation ... Abstract The values at 1 of single-valued multiple polylogarithms span a certain subalgebra of multiple zeta values. The properties of this algebra are studied from the point ... 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. dick butkus greatest hits youtube

ON POLYLOGARΠΉMS*

Category:[1902.03971] Holomorphic polylogarithms and Bloch complexes

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Polylogarithms pdf

(PDF) Cluster Polylogarithms - ResearchGate

http://people.mpim-bonn.mpg.de/stavros/publications/resurgencepolylogarithms.pdf WebDec 19, 2024 · A bstractWe introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic …

Polylogarithms pdf

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WebIn physics, polylogarithms appear in several ways. One way they appear is when computing Feynman integrals. Polylogarithms also appear in integrable models. For example, sup … Webdescribe the scattering of elementary particles, polylogarithms are ubiquitous. One way to understand the connection between polylogarithms and Feynman integrals is through the …

WebWe prove linear independence of indefinite iterated Eisenstein integrals over the fraction field of the ring of formal power series Z[[q]]. Our proof relies on a general criterium for linear independence of iterated integrals, which has been established by Deneufchâtel, Duchamp, Minh and Solomon. As a corollary, we obtain C-linear independence of indefinite iterated … http://www.numdam.org/item/ASNSP_2006_5_5_1_1_0.pdf

WebWe remark that the present extension from polylogarithms of rational numbers to polylogarithms of algebraic numbers is analogue to the extension made in [1], where Amoroso and Viola obtain good approximation measures for logarithms of algebraic numbers by generalizing a previous method of Viola [5] for logarithms of rational numbers. 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 …

WebCluster 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.

Web1.3. Quadrangular polylogarithms are cluster polylogarithms in type A. Exam-ples of cluster polylogarithms are not easy to construct because the conditions of cluster adjacency and … dick cepek mud terrain tiresWebApr 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 ... dick blick can lightsWebMar 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 … dick beardsley guidehttp://people.mpim-bonn.mpg.de/stavros/publications/resurgencepolylogarithms.pdf dichotic listening and shadowingWebFeb 3, 2024 · Integrals of inverse trigonometric and polylogarithmic functions. In this paper we study the representation of integrals whose integrand involves the product of a … dick doja cat 1 hourWebApr 14, 2024 · The main purpose of this paper is to define multiple alternative q-harmonic numbers, Hnk;q and multi-generalized q-hyperharmonic numbers of order r, Hnrk;q by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms … dick hotchkiss grass valley caWebMar 1, 2011 · PDF In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. ... Keywords: polylogarithms; zeta functions; ... dick brown audio cables