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Construction of siegel modular forms of degree three and commutation relations of Hecke operators

Published online by Cambridge University Press:  22 January 2016

Yoshio Tanigawa
Yoshio Tanigawa*
Affiliation:
Department of Mathematics Faculty of Science Nagoya University, Chikusa-ku, Nagoya 464, Japan
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In connection with the Shimura correspondence, Shintani [6] and Niwa [4] constructed a modular form by the integral with the theta kernel arising from the Weil representation. They treated the group Sp(1) × O(2, 1). Using the special isomorphism of O(2, 1) onto SL(2), Shintani constructed a modular form of half-integral weight from that of integral weight. We can write symbolically his case as “O(2, 1)→ Sp(1)” Then Niwa’s case is “Sp(l)→ O(2, 1)”, that is from the halfintegral to the integral. Their methods are generalized by many authors. In particular, Niwa’s are fully extended by Rallis-Schiffmann to “Sp(l)→O(p, q)”.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 100 , December 1985 , pp. 83 - 96
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

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