Polylogarithms pdf
Webpolylogarithms can be taken to genus one easily: iterated integrals on genus one allow for a natural shuffle multiplication and an associated coaction or symbol map [31]. Given the existence of the symbol map for elliptic iterated integrals, it is a natural problem to investigate functional relations for elliptic polylogarithms. http://people.mpim-bonn.mpg.de/stavros/publications/resurgencepolylogarithms.pdf
Polylogarithms pdf
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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 … 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
WebIt appears that the only known representations for the Riemann zeta function ((z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ((n) for any integer n > 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n > 1, by using 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 …
WebPOLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS Abdelmejid BAYAD and Yoshinori HAMAHATA (Received 18 February 2010) Abstract. In this paper we investigate special generalized Bernoulli polynomials that 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 …
WebApr 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 …
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 … dutch national flag problem 3-way partitionWebElliptic 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 … in 1790 native americans made upWebDec 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 … dutch narrowboatWebCluster 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. in 1796 what did the jay treaty accomplishWebWe 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. in 1796 edward jenner developed whatWebple 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 dutch national ballet rat kingWebdescribe the scattering of elementary particles, polylogarithms are ubiquitous. One way to understand the connection between polylogarithms and Feynman integrals is through the … in 1790 which city was more densely populated