Values of harmonic weak Maass forms on Hecke orbits

Dohoon Choi, Min Lee, Subong Lim

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)

    Abstract

    Let q:=e2πiz, where z∈H. For an even integer k, let f(z):=qhm=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.

    Original languageEnglish
    Pages (from-to)1046-1062
    Number of pages17
    JournalJournal of Mathematical Analysis and Applications
    Volume477
    Issue number2
    DOIs
    Publication statusPublished - 2019 Sept 15

    Bibliographical note

    Publisher Copyright:
    © 2019 Elsevier Inc.

    Keywords

    • Distribution
    • Harmonic weak Maass forms
    • Hecke orbits

    ASJC Scopus subject areas

    • Analysis
    • Applied Mathematics

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