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<p>The weight two Eisenstein series may be considered as the first example of a Katz <i>p</i>-adic modular form. Classically, its values are defined for the primes of ordinary reduction. We investigate a modified definition which applies uniformly to all primes of good reduction, both ordinary and supersingular. We show that, in the case of complex multiplication, these <i>p</i>-adic values coincide with the algebraic value of this Eisenstein series.</p>

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On the p-adic values of the weight two Eisenstein series for supersingular primes

  • 期刊论文

  • 发表日期：

    2025年9月5日

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  • P. Guerzhoy

摘要

The weight two Eisenstein series may be considered as the first example of a Katz p-adic modular form. Classically, its values are defined for the primes of ordinary reduction. We investigate a modified definition which applies uniformly to all primes of good reduction, both ordinary and supersingular. We show that, in the case of complex multiplication, these p-adic values coincide with the algebraic value of this Eisenstein series.