Additive twists and a conjecture by Mazur, Rubin and Stein

Nikolaos Diamantis; Jeffrey Hoffstein; Eren Mehmet Kıral; Min Lee

doi:10.1016/j.jnt.2019.11.016

Additive twists and a conjecture by Mazur, Rubin and Stein

Nikolaos Diamantis^*, Jeffrey Hoffstein, Eren Mehmet Kıral, Min Lee

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved. To cover levels that are important for elliptic curves, namely those that are not square-free, we establish results about L-functions with additive twists that are of independent interest.

Original language	English
Pages (from-to)	1-36
Number of pages	36
Journal	Journal of Number Theory
Volume	209
Early online date	17 Dec 2019
DOIs	https://doi.org/10.1016/j.jnt.2019.11.016
Publication status	Published - 1 Apr 2020

Keywords

Classical modular symbols
Mazur-Rubin-Stein conjecture

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title = "Additive twists and a conjecture by Mazur, Rubin and Stein",

abstract = "In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved. To cover levels that are important for elliptic curves, namely those that are not square-free, we establish results about L-functions with additive twists that are of independent interest.",

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AU - Kıral, Eren Mehmet

AU - Lee, Min

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AB - In this paper, a conjecture of Mazur, Rubin and Stein concerning certain averages of modular symbols is proved. To cover levels that are important for elliptic curves, namely those that are not square-free, we establish results about L-functions with additive twists that are of independent interest.

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KW - Mazur-Rubin-Stein conjecture

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