6 citations · 13 across the 6 of their papers we have counts for
7 papers · 1 filter
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…
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…
Differentiation Evens Out Zero Spacings
David W. Farmer, Robert C. Rhoades
If is a polynomial with all of its roots on the real line, then the roots of the derivative are more evenly spaced than the roots of . The same holds for a real entire…
Deformations of Maass forms
David W. Farmer, Stefan Lemurell
We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface under d…
Integral moments of L-functions
J. B. Conrey, D. W. Farmer, J. P. Keating +2
We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading…