The reciprocals of some characteristic 2 "theta series"
Number Theory
2011-07-22 v1
Abstract
Suppose l=2m+1, m>0. We introduce m "theta-series", [1],...,[m], in Z/2[[x]]. It has been conjectured that the n for which the coefficient of x^n in 1/[i] is 1 form a set of density 0. This is probably always false, but in certain cases, for n restricted to certain arithmetic progressions, it is true. We prove such zero-density results using the theory of modular forms, and speculate about what may be true in general.
Keywords
Cite
@article{arxiv.1107.4137,
title = {The reciprocals of some characteristic 2 "theta series"},
author = {Paul Monsky},
journal= {arXiv preprint arXiv:1107.4137},
year = {2011}
}
Comments
16 pages