A. Booker

activity

20122020

most citedSimple zeros of degree 2 L-functions

2 citations · 2 across the 3 of their papers we have counts for

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10 papers · 1 filter

math.NT2020

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.NT2019

Cracking the problem with 33

Andrew R. Booker

Inspired by the Numberphile video "The uncracked problem with 33" by Tim Browning and Brady Haran, we investigate solutions to $x^{3} + y^{3} + z^{3} = k$ for a few small values of $k$ . We fin…

math.NT2019

Test vectors for Rankin-Selberg $L$ -functions

Andrew R. Booker, M. Krishnamurthy, Min Lee

We study the local zeta integrals attached to a pair of generic representations $(π, τ)$ of $G L_{n} \times G L_{m}$ , $n > m$ , over a $p$ -adic field. Through a process of unipotent averaging…

math.NT2018

Quantitative estimates for simple zeros of L-functions

Andrew R. Booker, Micah B. Milinovich, Nathan Ng

We generalize a method of Conrey and Ghosh (Invent. Math. 94 (1988)) to prove quantitative estimates for simple zeros of modular form L-functions of arbitrary conductor.

math.NT2018

New integral representations for Rankin-Selberg L-functions

Andrew R. Booker, Muthu Krishnamurthy, Min Lee

We derive integral representations for the Rankin-Selberg L-functions on GL(3) x GL(1) and GL(3) x GL(2) by a process of unipotent averaging at archimedean places. A key feature of…