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Rankin-Selberg L-functions in cyclotomic towers, I

By Jeanine Van Order

Abstract

We formulate and in large part establish a general analogue Mazur's conjecture for central values of $\operatorname{GL}(2)$-Rankin-Selberg $L$-functions associated to modular elliptic curves. A sequel article shows how these results can be used to deduce the full conjecture in many cases using the existence of a related $p$-adic $L$-functions, and also how to deduce applications to bounding Mordell-Weil ranks of elliptic curves via the two-variable main conjectures of Iwasawa theory. The purpose of the present work however is to consider the problem via purely analytic methods, and to develop averaging techniques that should apply to a more general class of $L$-functions.Comment: 38 pp, revisions have been made to account for the fourth power Gauss sum appearing in the root numbe

Topics: Mathematics - Number Theory
Year: 2014
OAI identifier: oai:arXiv.org:1207.1672

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