Marc Munsch

activity

20142026

most citedShifted moments of L functions and moments of theta functions

12 citations · 20 across the 22 of their papers we have counts for

collaborators

Showing 2017Show all

4 papers · 1 filter

math.NT2017★ 3 cited

On smooth square-free numbers in arithmetic progressions

Marc Munsch, Igor E. Shparlinski

A. Booker and C. Pomerance (2017) have shown that any residue class modulo a prime $p \geq 11$ can be represented by a positive $p$ -smooth square-free integer $s = p^{O (l o g p)}$ wit…

math.NT2017

On the minimal number of small elements generating prime field

Marc Munsch

In this note, we give an upper bound for the number of elements from the interval $[1, p^{1/4 e^{1/2} + ε}]$ necessary to generate the finite field $F_{p}$ with $p$ an odd pri…

math.NT2017

Square-full primitive roots

Marc Munsch, Tim Trudgian

We use character sum estimates to give a bound on the least square-full primitive root modulo a prime. Specifically, we show that there is a square-full primitive root mod $p$ less…

math.NT2017

Extreme values of the Riemann zeta function on the 1-line

Christoph Aistleitner, Kamalakshya Mahatab, Marc Munsch

We prove that there are arbitrarily large values of $t$ such that $∣ ζ (1 + i t) ∣ \geq e^{γ} (lo g_{2} t + lo g_{3} t) + O (1)$ . This essentially matches the prediction for the optim…