6 citations · 13 across the 4 of their papers we have counts for
4 papers
Maass forms and their -functions
David W. Farmer, Stefan Lemurell
We present examples of Maass forms on Hecke congruence groups, giving low eigenvalues on for small prime , and the first 1000 eigenvalues for . We also present…
The maximum size of -functions
David W. Farmer, S. M. Gonek, C. P. Hughes
We conjecture the true rate of growth of the maximum size of the Riemann zeta function and other -functions. We support our conjecture using arguments from random matrix theory,…
Converse theorems assuming a partial Euler product
David W. Farmer, Kevin Wilson
Associated to a newform is a Dirichlet series with functional equation and Euler product. Hecke showed that if the Dirichlet series has a functional equation…
Basic analytic number theory
David W. Farmer
We give an informal introduction to the most basic techniques used to evaluate moments on the critical line of the Riemann zeta-function and to find asymptotics for sums of arithme…