The Pjateckii-Sapiro prime number theorem
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Publication:1050395
DOI10.1016/0022-314X(83)90044-6zbMath0513.10042MaRDI QIDQ1050395
Publication date: 1983
Published in: Journal of Number Theory (Search for Journal in Brave)
Special sequences and polynomials (11B83) Estimates on character sums (11L40) Primes in congruence classes (11N13) Distribution of primes (11N05)
Related Items (92)
On the Hardy-Littlewood majorant problem for arithmetic sets ⋮ On a binary Diophantine inequality involving prime numbers ⋮ AN ADDITIVE PROBLEM INVOLVING PIATETSKI-SHAPIRO PRIMES ⋮ On the fourth power moment of the error term for the divisor problem with congruence conditions ⋮ The quaternary Piatetski-Shapiro inequality with one prime of the form \(p = x^2 + y^2 + 1\) ⋮ The greatest prime factor of the integers in a short interval (III) ⋮ On the four-dimensional divisor problem of \((a,b,c,c)\) type ⋮ On a ternary Diophantine equation involving fractional powers with prime variables of a special form ⋮ On the mean value of a kind of zeta functions ⋮ On a tangent equation by primes ⋮ On the mean square of the error term for the asymmetric two-dimensional divisor problem. I ⋮ On an equation with prime numbers ⋮ On small fractional parts of perturbed polynomials ⋮ The distribution of r-free numbers ⋮ On a Diophantine inequality over primes. II ⋮ Unnamed Item ⋮ On the Piatetski-Shapiro-Vinogradov theorem ⋮ On square-full numbers in short intervals ⋮ A ternary Diophantine inequality involving primes ⋮ On a sum involving small arithmetic functions ⋮ A special triple exponential sum ⋮ Almost primes in Piatetski-Shapiro sequences ⋮ On a Diophantine equation with prime variables ⋮ On an equation by primes with one Linnik prime ⋮ On stationary phase integrals ⋮ A hybrid of two theorems of Piatetski-Shapiro ⋮ A ternary Diophantine inequality by primes with one of the form \(p= x^2 +y^2 +1\) ⋮ Unnamed Item ⋮ Weak type \((1,1)\) inequalities for discrete rough maximal functions ⋮ The three primes theorem with primes in the intersection of two Piatetski-Shapiro sets ⋮ Friable values of Piatetski-Shapiro sequences ⋮ Hua’s theorem with the primes in Piatetski-Shapiro prime sets ⋮ Rough values of Piatetski-Shapiro sequences ⋮ The distribution of \(k\)-free numbers ⋮ On a conjecture of Chowla and Walum ⋮ Quadratic residues and non-residues for infinitely many Piatetski-Shapiro primes ⋮ Roth's theorem and the Hardy-Littlewood majorant problem for thin subsets of primes ⋮ Variance of squarefull numbers in short intervals ⋮ Roth-type theorem for quadratic system in Piatetski-Shapiro primes ⋮ On a variant of the prime number theorem ⋮ Lattice points problem, equidistribution and ergodic theorems for certain arithmetic spheres ⋮ Piatetski-Shapiro primes in arithmetic progressions ⋮ The greatest prime factor of the integers in a short interval (IV) ⋮ A Bombieri-Vinogradov-type result for exponential sums over Piatetski-Shapiro primes ⋮ On multiple exponential sums and their applications ⋮ Uniform distribution of prime powers and sets of recurrence and van der Corput sets in \(\mathbb{Z}^k\) ⋮ Number of \(\mathcal B\)-free numbers in short intervals ⋮ Nombres premiers de la forme ⌊nc⌋ ⋮ On the \(k\)-dimensional Piatetski-Shapiro prime number theorem ⋮ On the distribution of \(p^\alpha\) modulo one ⋮ On sums of two coprime \(k\)-th powers. II ⋮ Small gaps between the Piatetski-Shapiro primes ⋮ Quadratic forms connected with Fourier coefficients of Maass cusp forms ⋮ Diophantine inequalities over Piatetski-Shapiro primes ⋮ Some Diophantine equations and inequalities with primes ⋮ On a Diophantine inequality involving prime numbers ⋮ On representations of error terms related to the derivatives for some Dirichlet series ⋮ On mean values of Dirichlet polynomials ⋮ An additive problem on Piatetski-Shapiro primes ⋮ Diophantine approximation by cubes of primes and an almost prime ⋮ On the simultaneous distribution of the fractional parts of different powers of prime numbers ⋮ On higher-power moments of the error term for the divisor problem with congruence conditions ⋮ On a binary additive problem involving fractional powers ⋮ On the mean square of the error term for the asymmetric two-dimensional divisor problems. II ⋮ The distribution of square-full integers ⋮ Distribution of cube-free numbers with form \([n^c\)] ⋮ A note on primes of the form \(\lfloor\alpha p+\beta\rfloor\) ⋮ Primitive roots for Pjateckii-Šapiro primes ⋮ Distribution of \(\alpha p^2\) modulo one with prime variable \(p\) of a special form ⋮ \(\ell^p(\mathbb Z)\)-boundedness of discrete maximal functions along thin subsets of primes and pointwise ergodic theorems ⋮ On a generalization of the Euler totient function ⋮ The distribution of square-full integers. II ⋮ On the distribution of squarefree numbers ⋮ Roth's theorem in the Piatetski-Shapiro primes ⋮ Diophantine approximation over Piatetski-Shapiro primes ⋮ On a Diophantine equation with prime numbers ⋮ A Diophantine inequality with four prime variables ⋮ A variant of the prime number theorem ⋮ An additive problem with prime numbers from a thin set ⋮ A generalization of Piatetski-Shapiro sequences ⋮ On the error term in Weyl's law for the Heisenberg manifolds. II ⋮ The distribution of square-free numbers of the form \([n^c\)] ⋮ Unnamed Item ⋮ On the distribution of square-full integers ⋮ On a Diophantine equation involving primes ⋮ On a ternary Diophantine inequality over primes ⋮ On sums of two coprime cubes ⋮ Some applications to zero density theorems for \(L\)-functions ⋮ On small fractional parts of polynomial-like functions ⋮ An additive problem over Piatetski-Shapiro primes and almost-primes ⋮ The ternary Goldbach problem with two Piatetski–Shapiro primes and a prime with a missing digit ⋮ A diophantine equation involving special prime numbers
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