Roth-type theorem for quadratic system in Piatetski-Shapiro primes

DOI10.1016/j.jnt.2023.10.012OpenAlexW4388968888MaRDI QIDQ6187113

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Publication date: 10 January 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2023.10.012

zbMATH Keywords

Roth theoremtransference principlePiatetski-Shapiro primerational quadratic system

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Quadratic and bilinear Diophantine equations (11D09) Sums over primes (11L20) Arithmetic combinatorics; higher degree uniformity (11B30)

Cites Work

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• On certain other sets of integers
• On \(\Lambda\) (p)-subsets of squares
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• Roth's theorem in the primes
• Roth's theorem on progressions revisited
• The Pjateckii-Sapiro prime number theorem
• On triples in arithmetic progression
• Roth's theorem in many variables
• Integer sets containing no arithmetic progressions
• Nombres premiers de la forme ⌊n^c⌋
• ROTH’S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS
• Translation invariant equations and the method of Sanders
• A quantitative improvement for Roth's theorem on arithmetic progressions: Table 1.
• Integer Sets Containing No Arithmetic Progressions
• On the Pjateckii-Sapiro Prime Number Theorem
• A Transference Approach to a Roth-Type Theorem in the Squares
• Roth–Waring–Goldbach
• Points Entiers Au Voisinage D'une Courbe, Sommes Trigonométriques Courtes ET Paires D'exposants
• Piatetski-Shapiro meets Chebotarev
• On Certain Sets of Integers
• On Certain Sets of Integers (II)
• Primes of the form \([n^ c\)]
• The distribution of square-free numbers

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