Arithmetic statistics of modular symbols

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Arithmetic statistics of modular symbols. / Petridis, Yiannis N.; Risager, Morten S.

I: Inventiones Mathematicae, Bind 212, Nr. 3, 06.2018, s. 997-1053.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Petridis, YN & Risager, MS 2018, 'Arithmetic statistics of modular symbols', Inventiones Mathematicae, bind 212, nr. 3, s. 997-1053. https://doi.org/10.1007/s00222-017-0784-7

APA

Petridis, Y. N., & Risager, M. S. (2018). Arithmetic statistics of modular symbols. Inventiones Mathematicae, 212(3), 997-1053. https://doi.org/10.1007/s00222-017-0784-7

Vancouver

Petridis YN, Risager MS. Arithmetic statistics of modular symbols. Inventiones Mathematicae. 2018 jun.;212(3):997-1053. https://doi.org/10.1007/s00222-017-0784-7

Author

Petridis, Yiannis N. ; Risager, Morten S. / Arithmetic statistics of modular symbols. I: Inventiones Mathematicae. 2018 ; Bind 212, Nr. 3. s. 997-1053.

Bibtex

@article{987b3d34551747cf8825499dff98320c,
title = "Arithmetic statistics of modular symbols",
abstract = "Mazur, Rubin, and Stein have recently formulated a series of conjecturesabout statistical properties of modular symbols in order to understandcentral values of twists of elliptic curve L-functions. Two of these conjecturesrelate to the asymptotic growth of the first and second moments of the modularsymbols. We prove these on average by using analytic properties of Eisensteinseries twisted by modular symbols. Another of their conjectures predicts theGaussian distribution of normalized modular symbols ordered according tothe size of the denominator of the cusps. We prove this conjecture in a refinedversion that also allows restrictions on the location of the cusps.",
author = "Petridis, {Yiannis N.} and Risager, {Morten S.}",
year = "2018",
month = jun,
doi = "10.1007/s00222-017-0784-7",
language = "English",
volume = "212",
pages = "997--1053",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer",
number = "3",

}

RIS

TY - JOUR

T1 - Arithmetic statistics of modular symbols

AU - Petridis, Yiannis N.

AU - Risager, Morten S.

PY - 2018/6

Y1 - 2018/6

N2 - Mazur, Rubin, and Stein have recently formulated a series of conjecturesabout statistical properties of modular symbols in order to understandcentral values of twists of elliptic curve L-functions. Two of these conjecturesrelate to the asymptotic growth of the first and second moments of the modularsymbols. We prove these on average by using analytic properties of Eisensteinseries twisted by modular symbols. Another of their conjectures predicts theGaussian distribution of normalized modular symbols ordered according tothe size of the denominator of the cusps. We prove this conjecture in a refinedversion that also allows restrictions on the location of the cusps.

AB - Mazur, Rubin, and Stein have recently formulated a series of conjecturesabout statistical properties of modular symbols in order to understandcentral values of twists of elliptic curve L-functions. Two of these conjecturesrelate to the asymptotic growth of the first and second moments of the modularsymbols. We prove these on average by using analytic properties of Eisensteinseries twisted by modular symbols. Another of their conjectures predicts theGaussian distribution of normalized modular symbols ordered according tothe size of the denominator of the cusps. We prove this conjecture in a refinedversion that also allows restrictions on the location of the cusps.

U2 - 10.1007/s00222-017-0784-7

DO - 10.1007/s00222-017-0784-7

M3 - Journal article

VL - 212

SP - 997

EP - 1053

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 3

ER -

ID: 200291620