Bombieri-type theorem for convolution of arithmetic functions on Number field

2018/04/11 by Pranendu Darbar, Darbar, Pranendu, Anirban Mukhopadhyay +1
Mathematics · #11R04 #11R44 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #math.NT #msc:11R04 #msc:11R44

paper · pdf · doi:10.48550/arxiv.1804.04246

10 pages, Comments are welcome

arxiv created 2018/04/11 · openalex publication_date 2018/04/11 · arxiv updated 2018/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be an imaginary quadratic number field of class number one and O_K be its ring of integers. We show that, if the arithmetic functions f, g:O_K→ ℂ both have level of distribution ϑ for some 0<ϑ≤ 1/2 then the Dirichlet convolution f*g also have level of distribution ϑ.

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