Estimate of periods on Hirzebruch–Zagier cycles

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Abstract

We study the period integrals of Maass forms restricted to Hirzebruch–Zagier cycles of Hilbert surfaces. In particular, we shall prove an upper bound for such integrals with respect to Laplace eigenvalues of Maass forms. In a special case, this leads to an upper bound for certain special L-values.

Original languageEnglish
Pages (from-to)50-66
Number of pages17
JournalJournal of Number Theory
Volume224
DOIs
Publication statusPublished - Jul 2021

Keywords

  • Hilbert surface
  • Hirzebruch-Zagier cycle
  • L-values
  • Maass forms
  • Period

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