Roth's theorem in the Piatetski-Shapiro primes

DOI10.4171/RMI/848zbMath1337.11069arXiv1305.0043MaRDI QIDQ748339

Mariusz Mirek

Publication date: 20 October 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.0043

zbMATH Keywords

arithmetic progressionsHardy-Littlewood majorant problemtrigonometric sumsdiscrete restriction

Mathematics Subject Classification ID

Goldbach-type theorems; other additive questions involving primes (11P32) Trigonometric and exponential sums (general theory) (11L03)

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Kloosterman sums with twice-differentiable functions ⋮ Minor arcs, mean values, and restriction theory for exponential sums over smooth numbers ⋮ A hybrid of two theorems of Piatetski-Shapiro ⋮ Weak type \((1,1)\) inequalities for discrete rough maximal functions ⋮ On classification of sequences containing arbitrarily long arithmetic progressions ⋮ Roth's theorem and the Hardy-Littlewood majorant problem for thin subsets of primes ⋮ Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres ⋮ Piatetski-Shapiro primes in arithmetic progressions ⋮ Arithmetic Progressions in the Graphs of Slightly Curved Sequences ⋮ Distributions of finite sequences represented by polynomials in Piatetski-Shapiro sequences ⋮ \(\ell^p(\mathbb Z)\)-boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems ⋮ A generalization of Piatetski-Shapiro sequences ⋮ On massive sets for subordinated random walks

Cites Work

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• Combinatorial theorems in sparse random sets
• On \(\Lambda\) (p)-subsets of squares
• A hybrid of theorems of Vinogradov and Piatetski-Shapiro
• Roth's theorem in the primes
• Roth's theorem on progressions revisited
• The Pjateckii-Sapiro prime number theorem
• On the Piatetski-Shapiro-Vinogradov theorem
• On triples in arithmetic progression
• The primes contain arbitrarily long arithmetic progressions
• Restriction theory of the Selberg sieve, with applications
• \(\ell^p(\mathbb Z)\)-boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems
• Distribution of primes in sequences of the form \([n^c\)]
• Integer Sets Containing No Arithmetic Progressions
• On the Pjateckii-Sapiro Prime Number Theorem
• Generational Relations for the Abstract Group Simply Isomorphic with the Linear Fractional Group in the GF[2″]
• Arithmetic progressions of length three in subsets of a random set
• ON IMPROVING ROTH'S THEOREM IN THE PRIMES
• Improving Roth's Theorem in the Primes
• Primes of the form \([n^ c\)]