Estimate of periods on Hirzebruch–Zagier cycles

Feng Su

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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
StatePublished - Jul 2021
Externally publishedYes

Bibliographical note

Funding Information:
The author is very grateful to Andre Reznikov and Binyong Sun for helpful discussions, and to Shouwu Zhang for communicating his result in [7] (joint with Dihua Jiang and Jianshu Li). The author thanks the referee for helpful suggestions. The work was partly supported by the National Natural Science Foundation of China (Grant No. 11901466 ) and the XJTLU Research Development Funding ( RDF-19-02-04 ).

Publisher Copyright:
© 2021 Elsevier Inc.


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


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