2018/06/27 by Chris Hall, Jonathan P. Keating, Edva Roditty-Gershon
Mathematics 路 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Arithmetic #Combinatorics #Conjugacy class #Degree (music) #Divisor (algebraic geometry) #Divisor function #Elliptic curve #Function (biology) #Limit (mathematics) #Mathematical analysis #Mathematics #Pure mathematics #math.NT
paper 路 pdf 路 doi:10.2140/ant.2019.13.19
published as Alg. Number Th. 13 (2019) 19-92
arxiv created 2018/06/27 路 openalex publication_date 2019/02/13 路 arxiv updated 2019/03/06 路 openalex created_date 2021/02/01 路 openalex updated_date 2026/06/11
We compute the variances of sums in arithmetic progressions of arithmetic functions associated with certain [math] -functions of degree 2 and higher in [math] , in the limit as [math] . This is achieved by establishing appropriate equidistribution results for the associated Frobenius conjugacy classes. The variances are thus related to matrix integrals, which may be evaluated. Our results differ significantly from those that hold in the case of degree-1 [math] -functions (i.e., situations considered previously using this approach). They correspond to expressions found recently in the number field setting assuming a generalization of the pair correlation conjecture. Our calculations apply, for example, to elliptic curves defined over [math] .