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.
Bibliographical noteFunding Information:
The author is very grateful to Andre Reznikov and Binyong Sun for helpful discussions, and to Shouwu Zhang for communicating his result in  (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 ).
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- Hilbert surface
- Hirzebruch-Zagier cycle
- Maass forms