MULTIDIMENSIONAL VAN DER CORPUT SETS AND SMALL FRACTIONAL PARTS OF POLYNOMIALS

DOI10.1112/S0025579318000529zbMath1432.11077arXiv1606.03049OpenAlexW3100421525MaRDI QIDQ3121307

Robert F. Tichy, Manfred G. Madritsch

Publication date: 15 March 2019

Published in: Mathematika (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.03049

zbMATH Keywords

exponential sumsDiophantine inequalitiesPiatetski-Shapiro sequenceHeilbronn theoremsmall fractional parts of polynomialsvan der Corput setsdistribution modulo $1$Heilbronn setsjointly intersective system of polynomialspseudo polynomialVinogradov theorem

Mathematics Subject Classification ID

Small fractional parts of polynomials and generalizations (11J54) Sums over primes (11L20) Weyl sums (11L15)

Related Items

On small fractional parts of perturbed polynomials ⋮ Simultaneous small fractional parts of polynomials ⋮ On small fractional parts of polynomial-like functions

Cites Work

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• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Van der Corput's difference theorem: some modern developments
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Uniform distribution of prime powers and sets of recurrence and van der Corput sets in \(\mathbb{Z}^k\)
• Sequences, discrepancies and applications
• Intersective polynomials and the polynomial Szemerédi theorem
• On a problem of Gelfond: the sum of digits of prime numbers
• On uniform distribution of subsequences
• Ruzsa's problem on sets of recurrence
• On uniform distribution of double sequences
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Van der Corput's difference theorem
• On uniformly distributed sequences of integers and Poincaré recurrence. II
• On uniformly distributed sequences of integers and Poincaré recurrence
• Small fractional parts of polynomials
• Small values of \(n^ 2\alpha\pmod 1\)
• On van der Corput property of shifted primes
• Uniform distribution of subpolynomial functions along primes and applications
• Intersective polynomials and Diophantine approximation. II
• Normality of the Thue-Morse sequence along Piatetski-Shapiro sequences. II
• On the fractional parts of a set of points. II
• Ergodic averaging sequences
• Intersective Polynomials and Diophantine Approximation
• Piatetski-Shapiro sequences via Beatty sequences
• The sum of digits of \lfloor n^c\rfloor
• On van der Corput property of squares
• Sárközy's theorem for P-intersective polynomials
• The distribution of αp modulo one
• On the Fractional Parts of θx ² and φx ²
• Some extremal functions in Fourier analysis
• Trigonometric sums over primes I
• On certain solutions of the diophantine equation x-y = p(z)
• Diophantine Inequalities with Mixed Powers (mod 1)
• On difference sets of sequences of integers. I
• New Estimates for Smooth Weyl Sums
• FRACTIONAL PARTS OF POLYNOMIALS OVER THE PRIMES
• Répartition des fonctions q-multiplicatives dans la suite $([n^c)_{n∈ ℕ}$, c > 1]
• Problems and Results on Intersective Sets
• Dynamical Systems and Uniform Distribution of Sequences
• Propriétés q-multiplicatives de la suite \lfloor n^c\rfloor, c>1
• Van der Corput sets in Z^d
• ON A THEOREM OF HEILBRONN
• ON THE FRACTIONAL PARTS OF θn^k AND φn^k
• On the fractional parts of a set of points
• ON THE DISTRIBUTION OF THE SEQUENCE n2  (mod 1)