Noam Kimmel

activity

20212025

collaborators

6 papers

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 wei…

math.NT2024

Vanishing of Poincaré series for congruence subgroups

Noam Kimmel

We consider the problem of the vanishing of Poincaré series for congruence subgroups. Denoting by $P_{k, m, N}$ the Poincaré series of weight $k$ and index $m$ for the group $Γ_{0} (N)$ …

math.NT2024

Positive density for consecutive runs of sums of two squares

Noam Kimmel, Vivian Kuperberg

We study the distribution of consecutive sums of two squares in arithmetic progressions. We show that for any odd squarefree modulus $q$ , any two reduced congruence classes $a_{1}$ a…

math.NT2024

Mass equidistribution for Poincaré series of large index

Noam Kimmel

Let $P_{k, m}$ denote the Poincaré series of weight $k$ and index $m$ for the full modular group $SL_{2} (Z)$ , and let ${P_{k, m}}$ be a sequence of Poincaré series…

math.NT2024

Asymptotic zeros of Poincaré series

Noam Kimmel

We study the zeros of Poincaré series $P_{k, m}$ for the full modular group. We consider the case where $m \sim α k$ for some constant $α > 0$ . We show that in this case a positive pr…

math.NT2021

Covariance of Error Terms Related to the Dirichlet Eigenvalue Problem

Noam Kimmel

We explore the covariance of error terms coming from Weyl's conjecture regarding the number of Dirichlet eigenvalues up to size $X$ . We also consider this problem in short interval…