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Fay's trisecant formula and cross-ratios

Author: Cris Poor
Journal: Proc. Amer. Math. Soc. 114 (1992), 667-671
MSC: Primary 14H42
MathSciNet review: 1062834
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Abstract: This note considers Fay's trisecant formula as a relation between cross-ratio functions and thereby gives a simple proof of the trisecant formula. In this proof the expression for the cross-ratio function is lifted from the theta locus to the entire Jacobian. Variations of the formula as used by different authors are also given.

References [Enhancements On Off] (What's this?)

  • [1] Hershel M. Farkas, On Fay’s tri-secant formula, J. Analyse Math. 44 (1984/85), 205–217. MR 801294,
  • [2] Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745
  • [3] John D. Fay, Theta functions on Riemann surfaces, Lecture Notes in Mathematics, Vol. 352, Springer-Verlag, Berlin-New York, 1973. MR 0335789
  • [4] R. C. Gunning, Lectures on Riemann surfaces, Jacobi varieties, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Mathematical Notes, No. 12. MR 0357407
  • [5] -, Lecture notes on theta functions. Parts $ A$ and $ B$, Princeton University (1987) (to appear in the next edition of 'Lectures on Riemann surfaces').
  • [6] R. C. Gunning, Some identities for abelian integrals, Amer. J. Math. 108 (1986), no. 1, 39–74 (1986). MR 821313,
  • [7] David Mumford, Tata lectures on theta. II, Progress in Mathematics, vol. 43, Birkhäuser Boston, Inc., Boston, MA, 1984. Jacobian theta functions and differential equations; With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura. MR 742776

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Keywords: Riemann surface, theta function, cross-ratio, trisecant formula
Article copyright: © Copyright 1992 American Mathematical Society