منابع مشابه
Thomae Type Formulae for Singular Z N Curves
We give an elementary and rigorous proof of the Thomae type formula for the singular curves µ N = m j=1 (λ − λ 2j) N−1 m j=0 (λ − λ 2j+1). To derive the Thomae formula we use the traditional variational method which goes back to Riemann, Thomae and Fuchs. An important step of the proof is the use of the Szegö kernel computed explicitly in algebraic form for non-singular 1/N-periods. The proof i...
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Expressions for the periods of first- and second-kind integrals on hyperelliptic curves are given in terms of theta-constants. They are derived with the help of Thomae's classical formulae and Picard-Fuchs equations for complete integrals as functions of the parameters of the curves. The example of genus 2 is considered in detail.
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We shall give an elementary and rigorous proof of the Thomae formula for ZN curves which was discovered by Bershadsky and Radul [1, 2]. Instead of using the determinant of the Laplacian we use the traditional variational method which goes back to Riemann, Thomae, Fuchs. In the proof we made explicit the algebraic expression of the chiral Szegö kernels and proves the vanishing of zero values of ...
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ژورنال
عنوان ژورنال: Moreana
سال: 1972
ISSN: 0047-8105,2398-4961
DOI: 10.3366/more.1972.9.2.20