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arXiv · 2403.04566

Pullback of arithmetic theta series and its modularity for unitary Shimura curves

Qiao He·Yousheng Shi·Tonghai Yang
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Abstract

This paper is a complement of the modularity result of Bruinier, Howard, Kudla, Rapoport and Yang (BHKRY) for the special case $U(1,1)$ not considered there. The main idea to embed a $U(1, 1)$ Shimura curve to many $U(n-1, 1)$ Shimura varieties for big $n$, and prove a precise pullback formula of the generating series of arithmetic divisors. Afterwards, we use the modularity result of BHKRY together with existence of non-vanishing of classical theta series at any given point in the upper half plane to prove the modulartiy result on $U(1, 1)$ Shimura curves.

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Qiao He, Yousheng Shi, Tonghai Yang. 2024-03-07. Pullback of arithmetic theta series and its modularity for unitary Shimura curves. https://arxiv.org/abs/2403.04566

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