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Biases amongst products of two Beatty primes in arithmetic progressions
Motivated by a recently observed bias in products of two prime numbers with congruence conditions by Dummit, Granville and Kisilevsky, we try to...
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Limitations to equidistribution in arithmetic progressions
In the spirit of the landmark work of Granville and Soundararajan, we further develop the theory of limitations to equidistribution in arithmetic...
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Rankin-Selberg coefficients in large arithmetic progressions
Let (λ f ( n )) n ⩾1 be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f . We prove that, for any fixed η >...
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Refinements to the prime number theorem for arithmetic progressions
We prove a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel–Walfisz theorem, Hoheisel’s...
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On infinite arithmetic progressions in sumsets
Let k be a positive integer. Denote by D 1/ k the least integer d such that for every set A of nonnegative integers with the lower density l/ k , the set...
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Euler Products with Primes in Progressions
As we have seen in Chap. 16 , in some Euler products, primes in a union of certain arithmetic...
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Arithmetic progressions of squares and multiple Dirichlet series
We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple...
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Sifting for small primes from an arithmetic progression
In this work and its sister paper (Friedlander and Iwaniec (2023)), we give a new proof of the famous Linnik theorem bounding the least prime in an...
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Sums of two unlike powers in arithmetic progressions
The variance associated with the distribution of sums of two unlike powers in arithmetic progressions is evaluated asymptotically.
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Primes in Arithmetical Progressions
We first gently steer the readers through the general notions and then inspect them more closely in two special cases.
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Monochromatic Arithmetic Progressions or Life After Van der Waerden’ Proof
And there was light: Issai Schur – who else – produced the first spark, a generalization of the Baudet–Schur–Van der Waerden Theorem. In fact, his...
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On Arithmetic Progressions in Model Sets
We establish the existence of arbitrary-length arithmetic progressions in model sets and Meyer sets in Euclidean d -space. We prove a van der...
