Let A(n) be the von Mangoldt function, let n ≥ 2 be an integer and let RG(n; q,a,b):= m1+m2=nm1amodqm2bmodqA(m1)A(m2) be the counting function for the Goldbach numbers with summands in arithmetic progression modulo a common integer q. We prove an asymptotic formula for the weighted average, with Cesàro weight of order k > 1, with k , of this function. Our result is uniform in a suitable range for q.
Cesàro averages for Goldbach representations with summands in arithmetic progressions / Cantarini, M.; Gambini, A.; Zaccagnini, A.. - In: INTERNATIONAL JOURNAL OF NUMBER THEORY. - ISSN 1793-0421. - 17:10(2021), pp. 2379-2393. [10.1142/S1793042121500937]
Cesàro averages for Goldbach representations with summands in arithmetic progressions
Gambini A.
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2021
Abstract
Let A(n) be the von Mangoldt function, let n ≥ 2 be an integer and let RG(n; q,a,b):= m1+m2=nm1amodqm2bmodqA(m1)A(m2) be the counting function for the Goldbach numbers with summands in arithmetic progression modulo a common integer q. We prove an asymptotic formula for the weighted average, with Cesàro weight of order k > 1, with k , of this function. Our result is uniform in a suitable range for q.| File | Dimensione | Formato | |
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