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On Some Results on Theta Constants (I)

Published online by Cambridge University Press:  22 January 2016

Hisasi Morikawa
Hisasi Morikawa*
Affiliation:
Mathematical Institute of Nagoya University and The John’s Hopkins University
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D. Mumford has shown an excelent algebralization of theory of theta constants and theta functions in his papers: On the equations defining abelian varieties I, II, III (Invent. Math. 1. 237-354 (1966), 3. 75-135 (1967), 3. 215-244) (1967). Our starting point and idea, however, are something different from those of Mumford; we begin our study at characterizing abelian addition formulae among all the possible addition formulae, and we want to give expressions to everything in words of matric notations.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 145 - 181
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

[I] Mumford, D., On the equations defining abelian varieties I, II, III, Invent. Math., 1 (1966), 287–354. 3 (1967), 75–135, 215–244.Google Scholar
[II] Weil, A., Sur certaines groupes d’operateurs unitaire, Acta Math., 111 (1964) 145–211.CrossRefGoogle Scholar
[III] Weil, A., Variétés abeliennes et courbes algébriques, Hermann, Paris, (1948).Google Scholar
[IV] Weil, A., Foundation of algebraic geometry, (1946).Google Scholar