A. Talmage

activity

20142022

most citedCoefficients and roots of peak polynomials

9 citations · 9 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2022

Prime Solutions of Diagonal Diophantine Systems

Alan Talmage

An asymptotic formula for the number of prime solutions of a general diagonal system of Diophantine equations is established, contingent on the existence of an appropriate mean val…

math.NT2019

Simultaneous Cubic and Quadratic Diagonal Equations In 12 Prime Variables

Alan Talmage

The system of equations \[ u_1p_1^2 + \ldots + u_sp_s^2 = 0 \] \[ v_1p_1^3 + \ldots + v_sp_s^3 = 0 \] has prime solutions $(p_{1}, \dots, p_{s})$ for $s \geq 12$ , assuming that the sy…

math.CO2014★ 9 cited

Coefficients and roots of peak polynomials

Sara Billey, Matthew Fahrbach, Alan Talmage

Given a permutation $π = π_{1} π_{2} \dots π_{n} \in S_{n}$ , we say an index $i$ is a peak if $π_{i - 1} < π_{i} > π_{i + 1}$ . Let $P (π)$ denote the set of peaks of $π$ . Given any set $S…