G. Martin

activity

19982023

most citedConstructions of Generalized Sidon Sets

26 citations · 124 across the 47 of their papers we have counts for

collaborators

62 papers

math.NT2023

A heuristic for discrete mean values of the derivative of the Riemann zeta function

Christopher Hughes, Greg Martin, Andrew Pearce-Crump

Shanks conjectured that $ζ^{'} (ρ)$ , where $ρ$ ranges over non-trivial zeros of the Riemann zeta function, is real and positive in the mean. We present a history of this problem, incl…

math.NT2021

Fake Mu's

Greg Martin, Michael J. Mossinghoff, Timothy S. Trudgian

Let $f (n)$ denote a multiplicative function with range ${- 1, 0, 1}$ , and let $F (x) = \sum_{n \leq x} f (n)$ . Then $F (x) / x = a x + b + E (x)$ , where $a$ and $b$ are consta…

math.NT2021

Multidimensional Padé approximation of binomial functions: Equalities

Michael A. Bennett, Greg Martin, Kevin O'Bryant

Let $ω_{0}, \dots, ω_{M}$ be complex numbers. If $H_{0}, \dots, H_{M}$ are polynomials of degree at most $ρ_{0}, \dots, ρ_{M}$ , and $G (z) = \sum_{m = 0}^{M} H_{m} (z) (1 - z)^{ω_{m}}$ has a zero at $z = 0$ of max…

math.NT2021

An algorithm for Egyptian fraction representations with restricted denominators

Greg Martin, Yue Shi

A unit fraction representation of a rational number $r$ is a finite sum of reciprocals of positive integers that equals $r$ . Of particular interest is the case when all denominator…

math.NT2021★ 2 cited

Asymptotics for the number of directions determined by $[n] \times [n]$ in $F_{p}^{2}$

Greg Martin, Ethan Patrick White, Chi Hoi Yip

Let $p$ be a prime and $n$ a positive integer such that $\frac{p}{2} + 1 \leq n \leq p$ . For any arithmetic progression $A$ of length $n$ in $F_{p}$ , we establish…

math.NT2020

Subproducts of small residue classes

Greg Martin, Amir Parvardi

For any prime $p$ , let $y (p)$ denote the smallest integer $y$ such that every reduced residue class $(mod p)$ is represented by the product of some subset of ${1, \dots, y}$ . It is…

A heuristic for discrete mean values of the derivative of the Riemann zeta function

Fake Mu's

Multidimensional Padé approximation of binomial functions: Equalities

An algorithm for Egyptian fraction representations with restricted denominators

Asymptotics for the number of directions determined by [n]×[n] in Fp2​

Subproducts of small residue classes

Asymptotics for the number of directions determined by $[n] \times [n]$ in $F_{p}^{2}$