کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594083 1335739 2013 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Artin representations attached to pairs of isogenous abelian varieties
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Artin representations attached to pairs of isogenous abelian varieties
چکیده انگلیسی

Given a pair of abelian varieties defined over a number field k and isogenous over a finite Galois extension L/k, we define a rational Artin representation of the group Gal(L/k) that shows a global relation between the L-functions of each variety and provides certain information about their decomposition up to isogeny over L. We study several properties of these Artin representations. As an application, for each curve C′ in a family of twists of a certain genus 3 curve C, we explicitly compute the Artin representation attached to the Jacobians of C and C′ and show how this Artin representation can be used to determine the L-function of the curve C′ in terms of the L-function of C. Moreover, from this Artin representation, we are able to compute the moments of the Sato–Tate distributions of the traces of the local factors of the curve C′.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 133, Issue 4, April 2013, Pages 1331-1345