GOLDBACH REPRESENTATIONS IN ARITHMETIC PROGRESSIONS AND ZEROS OF DIRICHLET L-FUNCTIONS. Issue 1 (24th August 2018)

• Record Type: Journal Article
• Authors: Bhowmik, Gautami; Halupczok, Karin; Matsumoto, Kohji; Suzuki, Yuta
• Is Part Of: Mathematika. Volume 65:Issue 1(2019)
• Page Start: 57
• Page End: 97
• Publication Date: 2018-08-24
• Subjects: 11P32, -- 11M26 (primary), -- 11M41 (secondary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579318000323
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract : Assuming a conjecture on distinct zeros of Dirichlet$L$ -functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression. On the other hand the existence of good error terms gives information on the location of zeros of$L$ -functions. Similar results are obtained for an integer in a congruence class expressed as the sum of two primes.