Open Access
Winter 2013 A theta expression of the Hilbert modular functions for 5 via the periods of K3 surfaces
Atsuhira Nagano
Kyoto J. Math. 53(4): 815-843 (Winter 2013). DOI: 10.1215/21562261-2366102

Abstract

In this paper, we give an extension of the classical story of the elliptic modular function to the Hilbert modular case for Q(5). We construct the period mapping for a family F={S(X,Y)} of K3 surfaces with 2 complex parameters X and Y. The inverse correspondence of the period mapping gives a system of generators of Hilbert modular functions for Q(5). Moreover, we show an explicit expression of this inverse correspondence by theta constants.

Citation

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Atsuhira Nagano. "A theta expression of the Hilbert modular functions for 5 via the periods of K3 surfaces." Kyoto J. Math. 53 (4) 815 - 843, Winter 2013. https://doi.org/10.1215/21562261-2366102

Information

Published: Winter 2013
First available in Project Euclid: 21 November 2013

zbMATH: 1285.14042
MathSciNet: MR3160602
Digital Object Identifier: 10.1215/21562261-2366102

Subjects:
Primary: 14J28
Secondary: 11F46 , 33C05

Rights: Copyright © 2013 Kyoto University

Vol.53 • No. 4 • Winter 2013
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