The spin of prime ideals
Number Theory
2012-10-23 v2
Abstract
Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in {0,1,-1}) that we call the "spin" and for which the associated L-function does not possess Euler products. We are nevertheless able, using the techniques of bilinear forms, to handle spin value distribution over primes, obtaining stronger results than the analogous ones which follow from the technology of L-functions in its current state. The initial application of our theorem is to the arithmetic statistics of Selmer groups of elliptic curves.
Keywords
Cite
@article{arxiv.1110.6331,
title = {The spin of prime ideals},
author = {J. B. Friedlander and H. Iwaniec and B. Mazur and K. Rubin},
journal= {arXiv preprint arXiv:1110.6331},
year = {2012}
}
Comments
Minor revisions. To appear in Inventiones Mathematicae