On the $p$-adic values of the weight two Eisenstein series for supersingular primes
Abstract
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 offer 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2024
- DOI:
- 10.48550/arXiv.2403.02592
- arXiv:
- arXiv:2403.02592
- Bibcode:
- 2024arXiv240302592G
- Keywords:
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- Mathematics - Number Theory;
- 11F33;
- 14H52;
- 11S31
- E-Print:
- 19 pages