L2(xy) where L2(z) is the famous single-valued dilogarithm. Similar identities in weight ... struction of the single-valued real analytic version of classical polylogarithms are given. ..... Proof. The lemma follows from the monodromy property of Ln(
Jun 30, 2016 - We summarize recent computations with a class of elliptic generalizations of polylogarithms, arising from the massive sunrise integral. For the ...
Oct 18, 2016 - For the sake of simplicity we shall assume that arg(q) = 0. The results derived ... It is immediately seen that ELi0;0 (x, y; q) has a pole at x = 1.
Sep 28, 2012 - arXiv:1209.6524v1 [hep-ph] 28 Sep 2012. Symbolic integration and multiple polylogarithms. Christian Bognerâa and Francis Brownab â .
On the other hand, as pointed out in [7, 8], âhigher cyclotomy theoryâ should study the multiple polylogarithm motives at roots of unity, not only those of the ...
Jan 2, 2017 - 5 The Leray spectral sequence for syntomic cohomology. 141. 5.1 Paranjape's ...... de Rham spectral sequence degenerates at E1. This is the ...
Aug 3, 2005 - α qqqq llllâ°â°â°â°â°â°â°â°â°â°â°â°â°â°. 66 66 zzzz. VV VV. Let us declare an arrow β of Dâ² â D as a new arrow of the dissection D. Denote.
[17, 19], âhigher cyclotomy theoryâ should study the multiple polylogarithm motives at roots of unity, not only those of the polylogarithms. For this reason we want ...
Article electronically published on October 11, 2000. SPECIAL ... is the usual polylogarithm [49], [50] when s is a positive integer and |b| ≥ 1. Of .... The first [38], [47],. ∞. ∑ ..... which experts in the field of basic hypergeometric series will
a multi-valued memomorhpic function on C. When n > 1 the special ...... fsâ1 n. (j ). (x(j sâ1. ))wr+1(x(js)) i . Here we took the liberty to drop the primes when it is ...
cyclotomy theoryâ should study the multiple polylogarithm motives at roots of unity, not only those of the polylogarithms. This is the primary reason for us to focus ...
Oct 5, 2012 - Phys. 267 (2006), 821-845, arXiv: math-ph/0602004. [16] A. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes, Math. Res.
Jan 11, 2013 - arXiv:1301.2584v1 [math.CA] 11 Jan 2013. Spherical Couplings and Multiple Elliptic Integrals. Yajun Zhou. PROGRAM IN APPLIED AND ...
Sep 16, 2017 - lutions of the nonlinear fractional elliptic problem. ... and important nonlocal operator is the fractional Laplacian operator arising in non-.
tant figures in mathematics had contributed to the development of these identities ... With the notation as above, Dn multiple RogersâRamanujan identities can be .... that case, one still needs to study possible overlaps and gaps between the lattic
Jun 3, 2003 - We call particular attention to the construction of lower solutions, which depends ..... parabolic cap in the center of the interval. An elementary ...
May 30, 2011 - It is given in analytic form in terms of series involving the Stirling numbers of the 2nd kind [36,37]. ...... Ï{5,3,1}. = â. 1. 3 â. 1. 5 Ï{1,0,â1} â Ï{5,1,â1} + Ï{5,1,1}. (5.124) Ï{5,4,1}. = â. 7 ...... [23] S. Lang,
Apr 29, 2013 - The technique of spherical rotation, which traces back to Beltrami's work on the Abel integral equations [Ref. 23, p. 328] ...... [7] Joseph Kleiber.
istence of multiple solutions for multivalued fourth order elliptic equations under Navier boundary conditions. Our main
Mar 1, 2016 - 1 Motivation: Multiple polylogarithms and Feynman integrals ... x3. 0 Ï2(x2). â« x2. 0 Ï1(x1). 1. arXiv:1603.00420v1 [hep-ph] 1 Mar 2016 ...
Kleene stars of the plane, polylogarithms and symmetries. G.H.E. Duchamp. 1. LIPN, University Paris Nord, 93800, Villetaneuse, France. V. Hoang Ngoc Minh. 2.
elliptic surface S and the corresponding fibre of the Jacobian fibration associated with S are of the same type. This will be discussed in a forthcoming paper.
Mathematical Research Letters 7, 729â746 (2000). AN ELLIPTIC ... This conjecture fits in rich line of research on mul- tiple basic hypergeometric series, see e.g. ...
Oct 31, 2011 - FRANCIS BROWN AND ANDREY LEVIN. Abstract. We study the de Rham fundamental group of the configuration space. E(n) of n+1 marked ...
MULTIPLE ELLIPTIC POLYLOGARITHMS
arXiv:1110.6917v1 [math.NT] 31 Oct 2011
FRANCIS BROWN AND ANDREY LEVIN Abstract. We study the de Rham fundamental group of the configuration space E (n) of n+1 marked points on an elliptic curve E, and define multiple elliptic polylogarithms. These are multivalued functions on E (n) with unipotent monodromy, and are constructed by a general averaging procedure. We show that all iterated integrals on E (n) , and in particular the periods of the unipotent fundamental group of the punctured curve E\{0}, can be expressed in terms of these functions.
1. Introduction 1.1. Motivation. Iterated integrals on the moduli space M0,n of curves of genus 0 with n ordered marked points can be expressed in terms of multiple polylogarithms. These are defined for n1 , . . . , nr ∈ N by X xk11 . . . xkr r (1.1) Lin1 ,...,nr (x1 , . . . , xr ) = where |xi | < 1 , k1n1 . . . krnr 0
