# Equidistribution from the Chinese Remainder Theorem

@article{Kowalski2021EquidistributionFT,
title={Equidistribution from the Chinese Remainder Theorem},
author={Emmanuel Kowalski and Kannan Soundararajan},
year={2021}
}
• Published 29 March 2020
• Mathematics
10 Citations
A note on pseudo-polynomials divisible only by a sparse set of primes
For certain arbitrarily sparse sets $R$, we construct pseudo-polynomials $f$ with $p|f(n)$ for some $n$ only if $p \in R$. This implies that not all pseudo-polynomials satisfy an assumption of a
Derangements and the $p$-adic incomplete gamma function.
• Mathematics
• 2020
We introduce a new $p$-adic analogue of the incomplete gamma function. We also introduce a closely related family of combinatorial sequences counting derangements and arrangements in certain wreath
On the Joint Distribution of the Roots of Pairs of Polynomial Congruences
Let f(x) be a primitive irreducible polynomial with integer coefficients of degree greater than one. In 1964, Hooley showed that the sequence of normalized roots u/n, where f(u) = 0(n), ordered in
Exponential sums, twisted multiplicativity and moments
• Mathematics
• 2021
We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of
Fine-scale distribution of roots of quadratic congruences
• Mathematics
• 2021
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence μ ≡ D mod m, with D > 0 square-free and D 6≡ 1 mod 4. This is achieved by translating the
Sectorial equidistribution of the roots of $x^2 + 1$ modulo primes
• Mathematics
• 2021
The equation x+1 = 0 mod p has solutions whenever p = 2 or 4n+1. A famous theorem of Fermat says that these primes are exactly the ones that can be described as a sum of two squares. That the roots
Structural results on lifting, orthogonality and finiteness of idempotents
• Mathematics
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• 2021
In this paper, using the canonical correspondence between the idempotents and clopens, we obtain several new results on lifting idempotents. The Zariski clopens of the maximal spectrum are precisely
On primary pseudo-polynomials (Around Ruzsa's Conjecture)
• Mathematics
• 2020
Every polynomial P (X) ∈ Z[X] satisfies the congruences P (n + m) ≡ P (n) mod m for all integers n,m ≥ 0. An integer valued sequence (an)n≥0 is called a pseudo-polynomial when it satisfies these
On pseudo-polynomials divisible only by a sparse set of primes and $\a$-primary pseudo-polynomials
We explore two questions about pseudo-polynomials, which are functions f : N → Z such that k divides f(n+ k)− f(n) for all n, k. First, for certain arbitrarily sparse sets R, we construct
Parameterizing roots of polynomial congruences
We use the arithmetic of ideals in orders to parameterize the roots $\mu \pmod m$ of the polynomial congruence $F(\mu) \equiv 0 \pmod m$, $F(X) \in \mathbb{Z}[X]$ monic, irreducible and degree $d$.

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A note on pseudo-polynomials divisible only by a sparse set of primes
For certain arbitrarily sparse sets $R$, we construct pseudo-polynomials $f$ with $p|f(n)$ for some $n$ only if $p \in R$. This implies that not all pseudo-polynomials satisfy an assumption of a
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Keywords: Kloosterman sums ; absolute value ; mean value ; exponential sums Reference TAN-ARTICLE-2003-002doi:10.2140/pjm.2003.209.261 Record created on 2008-11-14, modified on 2017-05-12