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On Gunning’s Prime Form in Genus 2

Published online by Cambridge University Press:  20 November 2018

David Grant
David Grant*
Affiliation:
Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309-0395, U.S.A., email: grant@boulder.colorado.edu
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Abstract

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Using a classical generalization of Jacobi’s derivative formula, we give an explicit expression for Gunning’s prime form in genus 2 in terms of theta functions and their derivatives.

Keywords

14K2530F10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 89 - 96
Copyright
Copyright © Canadian Mathematical Society 2002

References

[C] Coogan, G., A generalization of Jacobi's derivative formula. Ph.D. Thesis, University of Colorado at Boulder, 1999.Google Scholar
[F] Fay, J., Theta Functions on Riemann surfaces. LectureNotes inMath. 353, Springer-Verlag, Berlin, 1973.Google Scholar
[Gr] Grant, D., A generalization of Jacobi's derivative formula to dimension two. J. Reine Angew.Math. 392 (1988), 125–136.Google Scholar
[Gu1] Gunning, R. C., Riemann Surfaces and Generalized Theta Functions. Springer-Verlag, Berlin, 1976.Google Scholar
[Gu2] Gunning, R. C., On generalized theta functions. Amer. J.Math. (1) 104 (1982), 183–208.Google Scholar
[Gu3] Gunning, R. C., Some identities for abelian integrals. Amer. J.Math. 108 (1986), 39–74.Google Scholar
[Gu4] Gunning, R. C., Analytic identities for theta functions. Proc. Symp. Pure Math. (1) 49 (1989), 503–515.Google Scholar
[Gu5] Gunning, R. C., Notes from a course given at PrincetonUniversity. 1987–88.Google Scholar
[I] Igusa, J.-I., On Jacobi's Derivative Formula and its generalizations. Amer. J.Math. (2) 102 (1980), 409–446.Google Scholar
[M] Mumford, D., Tata Lectures on Theta, I, II. Prog. in. Math. 28, 43, Birkhauser, Boston, 1983, 1984.Google Scholar
[P] Poor, C., The hyperelliptic locus. Duke Math. J. (3) 76 (1994), 809–884.Google Scholar