Noam Kimmel

collaborators

6 papers

math.NT2025

Non-vanishing of PoincarÃ© Series on Average

Ned Carmichael, Noam Kimmel

We study when PoincarÃ© series for congruence subgroups do not vanish identically. We show that almost all PoincarÃ© series with suitable parameters do not vanish when either the w…

math.NT2025

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.NT2025

Mass equidistribution for PoincarÃ© series of large index

Noam Kimmel

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

math.NT2024

Consecutive runs of sums of two squares

Noam Kimmel, Vivian Kuperberg

We study the distribution of consecutive sums of two squares in arithmetic progressions. If ${E_{n}}_{n \in N}$ is the sequence of sums of two squares in increasing order,…

math.NT2024

Artin's Primitive Root Conjecture in Number Fields and For Matrices

Noam Kimmel

In 1927, E. Artin conjectured that all non-square integers $a \neq = - 1$ are a primitive root of $F_{p}$ for infinitely many primes $p$ . In 1967, Hooley showed that this conjec…

math.NT2024

Noam Kimmel

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

Non-vanishing of PoincarÃ© Series on Average

Positive density for consecutive runs of sums of two squares

Mass equidistribution for PoincarÃ© series of large index

Consecutive runs of sums of two squares

Artin's Primitive Root Conjecture in Number Fields and For Matrices

Asymptotic zeros of PoincarÃ© series