Letters in Mathematical Physics

, Volume 76, Issue 2, pp 187–214

Thomae Type Formulae For Singular ZN Curves


DOI: 10.1007/s11005-006-0073-7

Cite this article as:
Enolski, V.Z. & Grava, T. Lett Math Phys (2006) 76: 187. doi:10.1007/s11005-006-0073-7


We give an elementary and rigorous proof of the Thomae type formula for the singular curves \(\mu^N=\prod_{j=1}^m(\lambda-\lambda_{2j})^{N-1}\prod_{j=0}^{m}(\lambda-\lambda_{2j+1})\). 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 inherits principal points of Nakayashiki’s proof (Nakayashiki in Publ. Res. Inst. Math. Sci 33(6) 987–1015, 1997) obtained for non-singular ZN curves.

Mathematics Subject Classifications (2000)

35Q15 30F60 32G81 


Thomae type formula Riemann surfaces kernel forms Rauch variational formulas nonsingular characteristics 

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institute of Magnetism NASUKyivUkraine
  2. 2.SISSATriesteItaly

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