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

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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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10.1016/j.jnt.2019.11.016

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://www.sciencedirect.com/science/article/pii/S0022314X19304160 . Please refer to any applicable terms of use of the publisher.
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Cite this

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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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author = "Nikolaos Diamantis and Jeffrey Hoffstein and Kıral, {Eren Mehmet} and Min Lee",

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AU - Diamantis, Nikolaos

AU - Hoffstein, Jeffrey

AU - Kıral, Eren Mehmet

AU - Lee, Min

PY - 2020/4/1

Y1 - 2020/4/1

N2 - 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.

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.

KW - Classical modular symbols

KW - Mazur-Rubin-Stein conjecture

UR - http://www.scopus.com/inward/record.url?scp=85077203158&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2019.11.016

DO - 10.1016/j.jnt.2019.11.016

M3 - Article (Academic Journal)

AN - SCOPUS:85077203158

VL - 209

SP - 1

EP - 36

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

Additive twists and a conjecture by Mazur, Rubin and Stein

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Keywords

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