Vinogradov's three primes theorem with primes having given primitive roots

Christopher Frei, P Koymans, E Sofos

Research output: Contribution to journalArticlepeer-review


The first purpose of our paper is to show how Hooley's celebrated method leading to his conditional proof of the Artin conjecture on primitive roots can be combined with the Hardy-Littlewood circle method. We do so by studying the number of representations of an odd integer as a sum of three primes, all of which have prescribed primitive roots. The second purpose is to analyse the singular series. In particular, using results of Lenstra, Stevenhagen and Moree, we provide a partial factorisation as an Euler product and prove that this does not extend to a complete factorisation.

Original languageEnglish
Pages (from-to)75-110
Number of pages36
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number1
Publication statusPublished - Jan 2021
Externally publishedYes


  • 2010 Mathematics Subject Classification: 11P32 11P55 11R45

ASJC Scopus subject areas

  • Mathematics(all)


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