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Sasaki, Ryuji

An arithmetic of modular function fields of degree two. (English) Zbl 1024.11031

Acta Math. Inform. Univ. Ostrav. 7, No. 1, 79-105 (1999).
The aim of this article is to generalize results on fields of modular functions of higher level from [G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press (1971; Zbl 0221.10029)] to fields of Siegel modular functions of degree two. The method uses explicit quadratic relations for theta-functions. It should be noted that the final result (Theorem 3) follows from a general reciprocity law proved by G. Shimura [Acta Math. 141, 35-71 (1978; Zbl 0402.10030)]. However, the author’s explicit approach can also be of interest.
Reviewer: Jan Nekovář (Cambridge)

MSC:

11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
14K25 Theta functions and abelian varieties

Keywords:

Siegel modular forms; theta functions; Kummer surfaces

Citations:

Zbl 0221.10029; Zbl 0402.10030
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References:

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