Temple University
When
2 – 3 p.m., March 4, 2025
Where
Title: Eisenstein congruences in prime-square level
Abstract: In his celebrated Eisenstein ideal paper, Mazur studied congruences modulo a prime p between Eisenstein series and cusp forms in prime level N. If p is at least 5, he showed that such congruences exist if and only if N is congruent to 1 modulo p. I will discuss recent work with Preston Wake in which we investigate Eisenstein-cuspidal congruences when the level is N^2, where N is a prime congruent to -1 modulo p. We show that such congruences exist in this case, and that they are remarkably uniform compared with Mazur’s setting. Moreover, one can use a mild extension of Ribet’s method to produce from our congruences nontrivial elements in the class group of Q(N^{1/p}).