Some applications of Bombieri's theorem

Bombieri's mean value theorem

“…BOMBIERI'S MEAN VALUE THEOREM P. X. GALLAGHER The purpose of this paper is to give a short proof of an important recent theorem of Bombieri [2] on the mean value of the remainder term in the prime number theorem for arithmetic progressions. Applications of the theorem have been made by Bombieri and Davenport [3], Rodriques [9], and Elliott and Halberstam [5]. For earlier versions of the theorem and a survey of other applications, see Barban [1], and Halberstam and Roth [7,Chapter 4].…”

Nonnegative Multiplicative Functions on Sifted Sets, and the Square Roots of −1 Modulo Shifted Primes

“…Actually, Hooley's work was conditional on GRH, but the discovery of the Bombieri-Vinogradov theorem allowed for this dependence to be removed with minimal changes to Hooley's argument. See [6]. (In the intervening years, Linnik gave an alternative proof of Theorem B [13].)…”

Heini Halberstam, 1926-2014

“…Some random examples are Murty and Saidak 〈〉 and Xiong 〈〉.

‘The values of a trigonometrical polynomial at well spaced points’ (with H. Davenport, 1966) ; see also ‘Corrigendum and addendum: The values of a trigonometrical polynomial at well spaced points’ (1967) ‘Primes in arithmetic progressions’ (with H. Davenport, 1966) ; see also ‘Corrigendum: Primes in arithmetic progression’ (1968) ‘Footnote to the Titchmarsh–Linnik divisor problem’ (1967) ‘Some applications of Bombieri's theorem’ (with P. D. T. A. Elliott, 1966) ‘The large sieve’ (1968, published 1970) .

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