Consider the number of integers in a short interval that can be represented as a sum of two
squares. What is an estimate for the variance of these counts over random short intervals …

In a surprising recent work, Lemke Oliver and Soundararajan noticed how experimental data
exhibits erratic distributions for consecutive pairs of primes in arithmetic progressions, and …

An old open problem in number theory is whether the Chebotarev density theorem holds in
short intervals. More precisely, given a Galois extension $ E $ of $\mathbb {Q} $ with Galois …

Squarefree polynomials with prescribed coefficients - ScienceDirect Skip to main contentSkip
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We investigate a function field analogue of a recent conjecture on autocorrelations of sums
of two squares by Freiberg, Kurlberg, and Rosenzweig, which generalizes an older …

An explicit polynomial analogue of Romanoff's theorem - ScienceDirect Skip to main contentSkip
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The prime number theorem for arithmetic progressions tells us that there are asymptotically
as many primes congruent to $1\bmod 4$ as there are congruent to $3\bmod 4$. That being …

For $ B\in\mathbb {F} _q [T] $ of degree $2 n\geq 2$, consider the number of ways of writing
$ B= E^ 2+\gamma F^ 2$, where $\gamma\in\mathbb {F} _q^* $ is fixed, and $ E …

Keating and Rudnick studied the variance of the polynomial von Mangoldt function Λ: F q
[t]→ C in arithmetic progressions and short intervals using two equidistribution results by …

For a polynomial F (t, A 1,…, A n)∈ FF pt, A 1,…, A n (p being a prime number) we study the
factorization statistics of its specializations F\left (t, a_1, ..., a_n\right) ∈ F _p\left t\right F (t, a …