Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

نویسندگان
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Iterated integrals, diagonal cycles and rational points on elliptic curves

The theme of this article is the connection between the pro-unipotent fundamental group π1(X; o) of a pointed algebraic curve X, algebraic cycles, and special values of Lfunctions. The extension of mixed Hodge structures arising in the second stage in the lower central series of π1(X; o) gives rise to a supply of complex points on the Jacobian Jac(X) of X, indexed by Hodge cycles on X ×X. The m...

متن کامل

ON THE p-ADIC REALIZATION OF ELLIPTIC POLYLOGARITHMS FOR CM-ELLIPTIC CURVES

Let E be a CM-elliptic curve over Q with good ordinary reduction at a prime p ≥ 5. The purpose of this paper is to construct the p-adic elliptic polylogarithm of E, following the method of A. Beı̆linson and A. Levin. Our main result is that the specializations of this object at torsion points give the special values of the one-variable p-adic L-function of the Grössencharakter associated to E.

متن کامل

Towards Multiple Elliptic Polylogarithms

Contents 1. Introduction 1 1.1. History and motivation 1 1.2. What we do 3 1.3. Plan of the article 3 1.4. Conventions and notations 4 2. The De Rham fundamental groupoid of a punctured elliptic curve 5 2.1. Nilpotent vector bundles 5 2.2. Nilpotent connections with simple poles at the origin 6 3. A universal flat connection over the upper-half plane 10 3.1. Combinatorial conventions and lemmas...

متن کامل

Generalized Jacobian and Discrete Logarithm Problem on Elliptic Curves

Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...

متن کامل

Elliptic Nets and Points on Elliptic Curves

(2) hn divides hm whenever n divides m. They have attracted number theoretical and combinatorial interest as some of the simplest nonlinear recurrence sequences (see [3] for references), but for us their interest lives in the underlying geometry: Ward demonstrates that an elliptic divisibility sequence arises from any choice of elliptic curve over Q and rational point on that curve. Theorem 1 (...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of High Energy Physics

سال: 2018

ISSN: 1029-8479

DOI: 10.1007/jhep05(2018)093