# 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
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• 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
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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
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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
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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
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• Mathematics
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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
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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
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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 $d$.