A note on additive twists, reciprocity laws and quantum modular forms
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A note on additive twists, reciprocity laws and quantum modular forms. / Nordentoft, Asbjørn Christian.
In: Ramanujan Journal, Vol. 56, 2021, p. 151–162.Research output: Contribution to journal › Journal article › Research › peer-review
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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