2011/07/20 by Paul Monsky, Monsky, Paul
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1107.4137
16 pages
arxiv created 2011/07/20 · openalex publication_date 2011/07/20 · arxiv updated 2011/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 xn 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.