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2017 On pairs of $p$-adic $L$-functions for weight-two modular forms
Florian Sprung
Algebra Number Theory 11(4): 885-928 (2017). DOI: 10.2140/ant.2017.11.885

Abstract

The point of this paper is to give an explicit p-adic analytic construction of two Iwasawa functions, Lp(f,T) and Lp(f,T), for a weight-two modular form anqn and a good prime p. This generalizes work of Pollack who worked in the supersingular case and also assumed ap = 0. These Iwasawa functions work in tandem to shed some light on the Birch and Swinnerton-Dyer conjectures in the cyclotomic direction: we bound the rank and estimate the growth of the Šafarevič–Tate group in the cyclotomic direction analytically, encountering a new phenomenon for small slopes.

Citation

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Florian Sprung. "On pairs of $p$-adic $L$-functions for weight-two modular forms." Algebra Number Theory 11 (4) 885 - 928, 2017. https://doi.org/10.2140/ant.2017.11.885

Information

Received: 10 April 2016; Revised: 16 December 2016; Accepted: 13 January 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06735374
MathSciNet: MR3665640
Digital Object Identifier: 10.2140/ant.2017.11.885

Subjects:
Primary: 11G40
Secondary: 11F67, 11R23

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2017
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