Estimate of periods on Hirzebruch–Zagier cycles

Feng Su

doi:10.1016/j.jnt.2021.01.023

Estimate of periods on Hirzebruch–Zagier cycles

Feng Su

Xi'an Jiaotong-Liverpool University

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	50-66
Number of pages	17
Journal	Journal of Number Theory
Volume	224
DOIs	https://doi.org/10.1016/j.jnt.2021.01.023
State	Published - Jul 2021
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Inc.

Funding

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 ).

Funders	Funder number
XJTLU Research Development Funding	RDF-19-02-04
National Natural Science Foundation of China	11901466

Keywords

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

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10.1016/j.jnt.2021.01.023

Cite this

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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.",

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KW - Hilbert surface

KW - Hirzebruch-Zagier cycle

KW - L-values

KW - Maass forms

KW - Period

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Estimate of periods on Hirzebruch–Zagier cycles

Abstract

Bibliographical note

Funding

Keywords

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