Primes in Arithmetic Progressions

By Paul B. Garrett. Series and Products in the Development of Mathematics, 2011

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Citations in the corpus

Explicit bounds for primes in arithmetic progressions (2018, methodology): “Finally, to complement our main theorems, we should mention one last result, summarizing our computations for “small” values of the parameter x (and extending and generalizing Theorem 2 of Ramaré and Rumely [33]) : Theorem 1.”
The variance of the number of prime polynomials in short intervals and in residue classes (2012, result): “Among other results is the one due to Montgomery [15] and Hooley [8] asserting that for X/(logX)A < Q < X one has (1.”
Primes in intervals of bounded length (2014, background): “Indeed all previous work, breaking the √ x barrier, such as [17], [5]) uses these types of estimates.”
Variants of the Selberg sieve, and bounded intervals containing many primes (2014, methodology): “[16], [22], [7], [65]), and using GEHrθs (with A replaced by a much larger fixed constant A1) to control all remaining contributions, we obtain the claim (using the Siegel-Walfisz theorem, see e.”
Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions (2013, background): “[20] H. Montgomery, Primes in arithmetic progressions, Michigan Math.”
Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method (2015, unknown): “The method at work in Theorems 1.1, 1.2 and 1.5 is the dispersion method, which was pioneered by Linnik [ Lin63 ] and studied intensively in groundbreaking work of Bombieri, Fouvry, Friedlander and Iwaniec [ Fou82 , FI83 , BFI86 ] on primes in arithmetic progressions.”
Bounded gaps between primes (2014, methodology): “In the Type I and II estimates we combine the dispersion method in [5] and [1] with the factorization (2.”
Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture (2015, background): “avior of the partial sums of the Mobius function, is an important area of study, connected to many fundamental number theoretical problems, see e.g. classical works [W], [Sch] and more recent papers [RR], [HS]. Sarnak [Sa] conjectures that is uncorrelated to any sequence obtained by reading any con”
On the exponent of distribution of the ternary divisor function (2013, background): “Thirty years ago, this problem was considered in a series of papers by Bombieri, Fouvry, Friedlander and Iwaniec (see in particular [6, 4, 1, 2]) with the purpose of improving the exponent 1/2 in the classical Bombieri–Vinogradov theorem concerning the distribution of primes in arithmetic progressio”