This paper proves universality of the distribution of the smallest and largest gaps between
eigenvalues of generalized Wigner matrices, under some smoothness assumption for the …

The Möbius function μ (n) is known for containing limited information on the prime
factorization of n. Its known algorithms, however, are all based on factorization and hence …

Let $\lambda (n) $ and $\mu (n) $ denote the Liouville function and the M\" obius function,
respectively. In this study, relationships between the values of $\lambda (n) $ and $\lambda …

We report on two machine learning experiments in search of statistical relationships
between Dirichlet coefficients and root numbers or analytic ranks of certain low-degree $ L …

We define an axiomatic class of L L-functions extending the Selberg class. We show in
particular that one can recast the traditional conditions of an Euler product, analytic …

Building on work of Boneh, Durfee and Howgrave-Graham, we present a deterministic
algorithm that provably finds all integers p such that pr| N in time O (N 1/4 r+ ϵ) for any ϵ> 0 …

In one of his final research papers, Alan Turing introduced a method to certify the
completeness of a purported list of zeros of the Riemann zeta-function. In this paper we …

Let $ n= a^ 2b $, where $ b $ is square-free. In this paper we present an algorithm based on
class groups of binary quadratic forms that finds the square-free decomposition of $ n $, ie …

We describe an algorithm that, given an integral ideal $\mathfrak {A} $ in a number field $ K
$, finds the largest integer $ k\geqslant 1$ such that $\mathfrak {A} $ is a $ k $-th power, and …

arXiv:2310.16952v1 [math.GM] 25 Oct 2023 Squarefree Values Of Polynomials Page 1 arXiv:2310.16952v1
[math.GM] 25 Oct 2023 Squarefree Values Of Polynomials NA Carella Abstract This note …