Abstract
The existence of good codes coming from classical modular curves is substantiated by the following three phenomena:
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(i)
the existence of modular curves,i.e.,curves whose points have an interpretation as modular points;
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(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;
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(iii)
the Eichler-Selberg trace formula,which computes the trace of a Hecke operator on the space of modular forms.
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© 1999 Springer Science+Business Media New York
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Stepanov, S.A. (1999). Reductions of Modular Curves. In: Codes on Algebraic Curves. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4785-3_9
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DOI: https://doi.org/10.1007/978-1-4615-4785-3_9
Publisher Name: Springer, Boston, MA
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