A note on additive twists, reciprocity laws and quantum modular forms

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Standard

A note on additive twists, reciprocity laws and quantum modular forms. / Nordentoft, Asbjørn Christian.

I: Ramanujan Journal, Bind 56, 2021, s. 151–162.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Nordentoft, AC 2021, 'A note on additive twists, reciprocity laws and quantum modular forms', Ramanujan Journal, bind 56, s. 151–162. https://doi.org/10.1007/s11139-020-00270-1

APA

Nordentoft, A. C. (2021). A note on additive twists, reciprocity laws and quantum modular forms. Ramanujan Journal, 56, 151–162. https://doi.org/10.1007/s11139-020-00270-1

Vancouver

Nordentoft AC. A note on additive twists, reciprocity laws and quantum modular forms. Ramanujan Journal. 2021;56:151–162. https://doi.org/10.1007/s11139-020-00270-1

Author

Nordentoft, Asbjørn Christian. / A note on additive twists, reciprocity laws and quantum modular forms. I: Ramanujan Journal. 2021 ; Bind 56. s. 151–162.

Bibtex

@article{deb681eb933e4777b3eab88e0bbf677f,
title = "A note on additive twists, reciprocity laws and quantum modular forms",
abstract = "We prove that the central values of additive twists of a cuspidal L-function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau. From this, we deduce a reciprocity law for the twisted first moment of multiplicative twists of cuspidal L-functions, similar to reciprocity laws discovered by Conrey for the twisted second moment of Dirichlet L-functions. Furthermore, we give an interpretation of quantum modularity at infinity for additive twists of L-functions of weight 2 cusp forms in terms of the corresponding functional equations.",
keywords = "Additive twists, Holomorphic cusp forms, Quantum modular forms, Reciprocity laws",
author = "Nordentoft, {Asbj{\o}rn Christian}",
year = "2021",
doi = "10.1007/s11139-020-00270-1",
language = "English",
volume = "56",
pages = "151–162",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - A note on additive twists, reciprocity laws and quantum modular forms

AU - Nordentoft, Asbjørn Christian

PY - 2021

Y1 - 2021

N2 - We prove that the central values of additive twists of a cuspidal L-function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau. From this, we deduce a reciprocity law for the twisted first moment of multiplicative twists of cuspidal L-functions, similar to reciprocity laws discovered by Conrey for the twisted second moment of Dirichlet L-functions. Furthermore, we give an interpretation of quantum modularity at infinity for additive twists of L-functions of weight 2 cusp forms in terms of the corresponding functional equations.

AB - We prove that the central values of additive twists of a cuspidal L-function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drappeau. From this, we deduce a reciprocity law for the twisted first moment of multiplicative twists of cuspidal L-functions, similar to reciprocity laws discovered by Conrey for the twisted second moment of Dirichlet L-functions. Furthermore, we give an interpretation of quantum modularity at infinity for additive twists of L-functions of weight 2 cusp forms in terms of the corresponding functional equations.

KW - Additive twists

KW - Holomorphic cusp forms

KW - Quantum modular forms

KW - Reciprocity laws

UR - http://www.scopus.com/inward/record.url?scp=85088932704&partnerID=8YFLogxK

U2 - 10.1007/s11139-020-00270-1

DO - 10.1007/s11139-020-00270-1

M3 - Journal article

AN - SCOPUS:85088932704

VL - 56

SP - 151

EP - 162

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

ER -

ID: 249254674