A. Booker

activity

20052022

most citedA database of genus 2 curves over the rational numbers

50 citations · 176 across the 26 of their papers we have counts for

collaborators

31 papers

math.NT2022

An extension of Venkatesh's converse theorem to the Selberg class

Andrew R. Booker, Michael Farmer, Min Lee

We extend Venkatesh's proof of the converse theorem for classical holomorphic modular forms to arbitrary level and character. The method of proof, via the Petersson trace formula,…

math.NT2021

Primitive elements with prescribed traces

Andrew R. Booker, Stephen D. Cohen, Nicol Leong +1

Given a prime power $q$ and a positive integer $n$ , let $F_{q^{n}}$ denote the finite field with $q^{n}$ elements. Also let $a, b$ be arbitrary members of the ground field $\…

math.NT2021

Wolstenholme and Vandiver primes

Andrew R. Booker, Shehzad Hathi, Michael J. Mossinghoff +1

A prime $p$ is a Wolstenholme prime if $(p 2 p) \equiv 2$ mod $p^{4}$ , or, equivalently, if $p$ divides the numerator of the Bernoulli number $B_{p - 3}$ ; a Vandiver prime $p$ is o…

math.NT2020★ 16 cited

On a question of Mordell

Andrew R. Booker, Andrew V. Sutherland

We make several improvements to methods for finding integer solutions to $x^{3} + y^{3} + z^{3} = k$ for small values of $k$ . We implemented these improvements on Charity Engine's global compu…

math.NT2020

On a recursively defined sequence involving the prime counting function

Altug Alkan, Andrew R. Booker, Florian Luca

We prove some properties of the sequence ${a_{n}}_{n \geq 1}$ defined by $a_{n} = π (n) - π (\sum_{k = 1}^{n - 1} a_{k}) .$

math.NT2020★ 19 cited

Computing classical modular forms

Alex J. Best, Jonathan Bober, Andrew R. Booker +8

We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).