TY - JOUR
T1 - On the Rankin–Selberg problem
AU - Huang, Bingrong
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/12
Y1 - 2021/12
N2 - In this paper, we solve the Rankin–Selberg problem. That is, we break the well known Rankin–Selberg’s bound on the error term of the second moment of Fourier coefficients of a GL (2) cusp form (both holomorphic and Maass), which remains its record since its birth for more than 80 years. We extend our method to deal with averages of coefficients of L-functions which can be factorized as a product of a degree one and a degree three L-functions.
AB - In this paper, we solve the Rankin–Selberg problem. That is, we break the well known Rankin–Selberg’s bound on the error term of the second moment of Fourier coefficients of a GL (2) cusp form (both holomorphic and Maass), which remains its record since its birth for more than 80 years. We extend our method to deal with averages of coefficients of L-functions which can be factorized as a product of a degree one and a degree three L-functions.
UR - http://www.scopus.com/inward/record.url?scp=85106464404&partnerID=8YFLogxK
U2 - 10.1007/s00208-021-02186-7
DO - 10.1007/s00208-021-02186-7
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AN - SCOPUS:85106464404
SN - 0025-5831
VL - 381
SP - 1217
EP - 1251
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -