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On the dimension of the vector space C[θm]4

Published online by Cambridge University Press:  22 January 2016

Riccardo Salvati Manni
Riccardo Salvati Manni*
Affiliation:
Dipartimento di Matematica, Università di Roma, Piazzale Aldo Horo, Roma, Italia
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Let τ denote a point of the Siegel upper-half space be a (column) vector in Cg and m a vector with m′ resp. m″ in Zg as its first resp. second entry vectors, then the series

in which , represents an holomorphic function on the product and it is called the theta function of characteristic m.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 98 , June 1985 , pp. 99 - 107
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Fay, J., On the Riemann-Jacobi formula, Göttingen Nachrichten, (1979), 61–73.Google Scholar
[ 2 ] Igusa, I., On the graded ring of theta constants, Amer. J. Math., 86 (1964), 219–246.Google Scholar
[ 3 ] Igusa, I., On Jacobi’s derivative formula and its generalizations, Amer. J. Math., 102 (1980), 409–446.Google Scholar
[ 4 ] Igusa, I., Theta Functions, Grund, math. Wiss., 194, Springer-Verlag, 1972.Google Scholar
[ 5 ] Igusa, I., Schottky’s invariant and quadratic forms, Christoffel Symposium, Birkhäuser Verlag (1981).Google Scholar
[ 6 ] Igusa, I., On the nullwerte of Jacobians of odd theta functions, preprint.Google Scholar
[ 7 ] Krazer, A., Lehrbuch der Thetafunktionen, B. G. Teubner, Leipzig, 1903.Google Scholar
[ 8 ] van Geemen, B., Siegel Modular forms vanishing on the Moduli space of curves, preprint (1983).Google Scholar