## Evidence for a Spectral Interpretation of the Zeros of L-Functions (1998)

Citations: | 33 - 7 self |

### BibTeX

@TECHREPORT{Rubinstein98evidencefor,

author = {Michael Oded Rubinstein},

title = {Evidence for a Spectral Interpretation of the Zeros of L-Functions},

institution = {},

year = {1998}

}

### Years of Citing Articles

### OpenURL

### Abstract

By looking at the average behavior (n-level density) of the low lying zeros of certain families of L-functions, we find evidence, as predicted by function field analogs, in favor of a spectral interpretation of the non-trivial zeros in terms of the classical compact groups. This is further supported by numerical experiments for which an efficient algorithm to compute L-functions was developed and implemented. iii Acknowledgements When Mike Rubinstein woke up one morning he was shocked to discover that he was writing the acknowledgements to his thesis. After two screenplays, a 40000 word manifesto, and many fruitless attempts at making sushi, something resembling a detailed academic work has emerged for which he has people to thank. Peter Sarnak- from Chebyshev's Bias to USp(1). For being a terrific advisor and teacher. For choosing problems suited to my talents and involving me in this great project to understand the zeros of L-functions. Zeev Rudnick and Andrew Oldyzko for many disc...