The reciprocals of some characteristic 2 "theta series"

Details The reciprocals of some characteristic 2 "theta series" The reciprocals of some characteristic 2 "theta series"

2011-07-20

arxiv.org/abs/1107.4137v1

Mathematics

Number Theory

16 pages

Scientific paper

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.

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