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.
|Number of pages||36|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - Jan 2021|
- 2010 Mathematics Subject Classification: 11P32 11P55 11R45
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