Reductions of Modular Curves

Serguei A. Stepanov
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Serguei A. Stepanov: Bilkent University

Chapter Chapter 9 in Codes on Algebraic Curves, 1999, pp 219-240 from Springer

Abstract: Abstract The existence of good codes coming from classical modular curves is substantiated by the following three phenomena: (i) the existence of modular curves,i.e.,curves whose points have an interpretation as modular points; (ii) the zeta-function of such curves overF p is expressible in terms of Fourier coefficients of normalized eigenforms for the algebra of Hecke operators; (iii) the Eichler-Selberg trace formula,which computes the trace of a Hecke operator on the space of modular forms.

Date: 1999
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DOI: 10.1007/978-1-4615-4785-3_9

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