Subsequences of primes in residue classes to prime moduli

1983 ◽  
pp. 157-164 ◽  
Author(s):  
P. D. T. A. Elliott
Keyword(s):  
Residue Classes

scholarly journals Not Distributive Lattice Over Field of Residue Classes Modulo 5

2020 ◽  
Vol V9 (05) ◽  
Author(s):  
T. Srinivasarao ◽  
Dr. V. Mallipriya ◽  
Keyword(s):  
Distributive Lattice ◽  
Residue Classes

scholarly journals A note on primes in certain residue classes

2018 ◽  
Vol 14 (08) ◽  
pp. 2219-2223
Author(s):  
Paolo Leonetti ◽  
Carlo Sanna
Keyword(s):  
Positive Integer ◽  
Asymptotic Density ◽  
Residue Classes ◽  
Euler Totient Function ◽  
The One ◽  
Positive Integers

Given positive integers [Formula: see text], we prove that the set of primes [Formula: see text] such that [Formula: see text] for [Formula: see text] admits asymptotic density relative to the set of all primes which is at least [Formula: see text], where [Formula: see text] is the Euler totient function. This result is similar to the one of Heilbronn and Rohrbach, which says that the set of positive integer [Formula: see text] such that [Formula: see text] for [Formula: see text] admits asymptotic density which is at least [Formula: see text].

scholarly journals Additive correlation and the inverse problem for the large sieve

2018 ◽  
Vol 168 (2) ◽  
pp. 211-217
Author(s):  
BRANDON HANSON
Keyword(s):  
Inverse Problem ◽  
Energy Estimate ◽  
Large Sieve ◽  
Residue Classes ◽  
Formula Group ◽  
Additive Energy ◽  
Image Position

AbstractLet A ⊆ [1, N] be a set of integers with |A| ≫ $\sqrt N$. We show that if A avoids about p/2 residue classes modulo p for each prime p, then A must correlate additively with the squares S = {n2 : 1 ≤ n ≤ $\sqrt N$}, in the sense that we have the additive energy estimate $$ E(A,S)\gg N\log N. $$ This is, in a sense, optimal.

Erratum: Limiting properties of the distribution of primes in an arbitrarily large number of residue classes

2020 ◽  
pp. 1-4
Author(s):  
Lucile Devin
Keyword(s):  
Linear Relation ◽  
Distribution Of Primes ◽  
Residue Classes

Abstract As pointed out by Alexandre Bailleul, the paper mentioned in the title contains a mistake in Theorem 2.2. The hypothesis on the linear relation of the almost periods is not sufficient. In this note, we fix the problem and its minor consequences on other results in the same paper.

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