Zeta-Functions of Modular Curves

  • Piateckii-Shapiro I. I. 
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 349)


This work gives an exposition and a generalization of classical results due to M. Eichler [1] and G. Shimura [2], which give the expression of congruence-zeta-functions of some modular curves in terms of Hecke polynomials. The central point in these papers is the famous congruence relation which links the local factor of the Mellin transforms of eigenfunctions of Hecke operators with the characteristic polynomial of Frobenius.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  • Piateckii-Shapiro I. I. 
    • 1
  1. 1.Laboratory of Math.Methods in Biology Corpus “A”Moscow State UniversityMoscowUSSR

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