A. Zaharescu

activity

19992025

most citedThe distribution of spacings between the fractional parts of

n^{2} α

108 citations · 307 across the 89 of their papers we have counts for

collaborators

Showing 2015Show all

5 papers · 1 filter

math.NT2015★ 2 cited

Continuous Distribution Arising From the Three Gaps Theorem

Geremías Polanco, Daniel Schultz, Alexandru Zaharescu

The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts ${α n}_{n < N}$ . It is known that if one averages over α, the dis…

math.NT2015★ 8 cited

A growth model based on the arithmetic $Z$ -game

Cristian Cobeli, Mihai Prunescu, Alexandru Zaharescu

We present an evolutionary self-governing model based on the numerical atomic rule $Z (a, b) = ab / g cd (a, b)^{2}$ , for $a, b$ positive integers. Starting with a sequence of numbers, the in…

math.NT2015

A Generalization of the Schur-Siegel-Smyth Trace Problem

Kyle Pratt, George Shakan, Alexandru Zaharescu

Let $α$ be a totally positive algebraic integer, and define its absolute trace to be $\frac{T r ( α )}{deg ( α )}$ , the trace of $α$ divided by the degree of $α$ . Elementary consid…

math.NT2015★ 2 cited

Simultaneous distribution of fractional parts of Riemann zeta zeros

Kevin Ford, Xianchang Meng, Alexandru Zaharescu

We investigate the simultaneous distribution of the fractional parts of ${α_{1} γ, α_{2} γ, \dots, α_{n} γ}$ , where $n \geq 2$ , $α_{1}$ , $α_{2}$ , $\dots$ , $α_{n}$ are fixed, distinct positive…

math.NT2015

Koshliakov kernel and identities involving the Riemann zeta function

Atul Dixit, Nicolas Robles, Arindam Roy +1

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z} (x), Y_{z} (x)$ and $K_{z} (x)$ are studied. In…

Continuous Distribution Arising From the Three Gaps Theorem

A growth model based on the arithmetic Z-game

A Generalization of the Schur-Siegel-Smyth Trace Problem

Simultaneous distribution of fractional parts of Riemann zeta zeros

Koshliakov kernel and identities involving the Riemann zeta function

A growth model based on the arithmetic $Z$ -game