David W. Farmer

most citedMaass forms and their

L

-functions

6 citations · 13 across the 4 of their papers we have counts for

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math.NT2005★ 6 cited

Maass forms and their $L$ -functions

David W. Farmer, Stefan Lemurell

We present examples of Maass forms on Hecke congruence groups, giving low eigenvalues on $Γ_{0} (p)$ for small prime $p$ , and the first 1000 eigenvalues for $Γ_{0} (11)$ . We also present…

math.NT2005★ 4 cited

The maximum size of $L$ -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 $L$ -functions. We support our conjecture using arguments from random matrix theory,…

math.NT2004★ 3 cited

Converse theorems assuming a partial Euler product

David W. Farmer, Kevin Wilson

Associated to a newform $f (z)$ is a Dirichlet series $L_{f} (s)$ with functional equation and Euler product. Hecke showed that if the Dirichlet series $F (s)$ has a functional equation…

math.NT2004

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…

math.NT2003★ 2 cited

Differentiation Evens Out Zero Spacings

David W. Farmer, Robert C. Rhoades

If $f$ is a polynomial with all of its roots on the real line, then the roots of the derivative $f^{'}$ are more evenly spaced than the roots of $f$ . The same holds for a real entire…