2022.04.12 14:18

# [SNU Number Theory Seminar 2022-04-15] A note on non-ordinary primes for some genus-zero arithmetic groups

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일정시작 2022-04-15 #FF5733
• Date :  2022-04-15  (Fri) 16:00

• Place :  27-325 (SNU)

• Speaker :  Seokho Jin (Chung-Ang University)
• Title :   A note on non-ordinary primes for some genus-zero arithmetic groups
• Abstract :   Suppose that O_L is the ring of integers of a number field L, and suppose that f(z) is a normalized Hecke eigenform for Γ0(N)+. We say that f is non-ordinary at p if there is a prime ideal p ⊂ OL above p for which a_f(p) ≡ 0 (mod p). In authors’ previous paper it was proved that there are infinitely many Hecke eigenforms for SL2(Z) such that are non-ordinary at any given finite set of primes. In this talk, we extend this result to some genus 0 subgroups of SL2(R), namely, the normalizers Γ0(N)+ of the congruence subgroups Γ0(N). This is joint with Wenjun Ma.

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