3 papers
math.NT2026
The Second Moment of Sums of Hecke Eigenvalues I
Ned Carmichael
Let be a holomorphic Hecke cusp form of weight for , and let denote its sequence of Hecke eigenvalues. We compute the first…
math.NT2026
The Second Moment of Sums of Hecke Eigenvalues II
Ned Carmichael
Let be a holomorphic Hecke cusp form of weight for , and let denote its sequence of normalised Hecke eigenvalues. We comput…
math.NT2025
Non-vanishing of Poincaré Series on Average
Ned Carmichael, Noam Kimmel
We study when Poincaré series for congruence subgroups do not vanish identically. We show that almost all Poincaré series with suitable parameters do not vanish when either the w…