The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer

Alessandra Migliaccio; Alessandro Zaccagnini

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arXiv · 2610.08285

The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer

Alessandra Migliaccio·Alessandro Zaccagnini

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Abstract

We extend a result by Ikeda and Suriajaya (2025) to the average number of representations of an integer as a sum of an arbitrary number $j\ge 3$ of primes. We show that the corresponding asymptotic formula holds in the general case. In the proof we use new ingredients like averages for the singular series of the generalized Goldbach problem.

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Alessandra Migliaccio, Alessandro Zaccagnini. 2026-10-06. The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer. https://arxiv.org/abs/2610.08285

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