TY - JOUR
T1 - Values of harmonic weak Maass forms on Hecke orbits
AU - Choi, Dohoon
AU - Lee, Min
AU - Lim, Subong
N1 - Funding Information:
D. Choi was partially supported by the National Research Foundation of Korea (NRF)grant (NRF-2019R1A2C1007517). M. Lee was supported by Royal Society University Research Fellowship “Automorphic forms, L-functions and trace formulas”. S. Lim was supported by the National Research Foundation of Korea (NRF)grant (NRF-2019R1C1C1009137).
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/9/15
Y1 - 2019/9/15
N2 - Let q:=e2πiz, where z∈H. For an even integer k, let f(z):=qh∏m=1 ∞(1−qm)c(m) be a meromorphic modular form of weight k on Γ0(N). For a positive integer m, let Tm be the mth Hecke operator and D be a divisor of a modular curve with level N. Both subjects, the exponents c(m)of a modular form and the distribution of the points in the support of Tm.D, have been widely investigated. When the level N is one, Bruinier, Kohnen, and Ono obtained, in terms of the values of j-invariant function, identities between the exponents c(m)of a modular form and the points in the support of Tm.D. In this paper, we extend this result to general Γ0(N)in terms of values of harmonic weak Maass forms of weight 0. By the distribution of Hecke points, this applies to obtain an asymptotic behavior of convolutions of sums of divisors of an integer and sums of exponents of a modular form.
AB - Let q:=e2πiz, where z∈H. For an even integer k, let f(z):=qh∏m=1 ∞(1−qm)c(m) be a meromorphic modular form of weight k on Γ0(N). For a positive integer m, let Tm be the mth Hecke operator and D be a divisor of a modular curve with level N. Both subjects, the exponents c(m)of a modular form and the distribution of the points in the support of Tm.D, have been widely investigated. When the level N is one, Bruinier, Kohnen, and Ono obtained, in terms of the values of j-invariant function, identities between the exponents c(m)of a modular form and the points in the support of Tm.D. In this paper, we extend this result to general Γ0(N)in terms of values of harmonic weak Maass forms of weight 0. By the distribution of Hecke points, this applies to obtain an asymptotic behavior of convolutions of sums of divisors of an integer and sums of exponents of a modular form.
KW - Distribution
KW - Harmonic weak Maass forms
KW - Hecke orbits
UR - http://www.scopus.com/inward/record.url?scp=85065546580&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2019.04.074
DO - 10.1016/j.jmaa.2019.04.074
M3 - Article
AN - SCOPUS:85065546580
SN - 0022-247X
VL - 477
SP - 1046
EP - 1062
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -