2013/12/05 by Jakob Johann Ditchen, Ditchen, Jakob
Mathematics · #11N05 #11N32 #11N36 #11N75 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1312.1502
openalex publication_date 2013/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the average distribution of primes represented by positive definite integral binary quadratic forms, the average being taken over negative fundamental discriminants in long ranges. In particular, we prove corresponding results of Bombieri-Vinogradov type and of Barban-Davenport-Halberstam type, although with shorter ranges than in the original theorems for primes in arithmetic progressions: The results imply that, for all a>0, the least prime that can be represented by any given positive definite binary quadratic form of discriminant q is smaller than |q|7+a for all forms to "most" discriminants; moreover, it is even smaller than |q|3+a for "most" forms to "most" discriminants.