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A Bound for Prime Solutions of Some Ternary Equations.

Ming-Chit Liu (1984/1985)

Mathematische Zeitschrift

A diophantine inequality involving prime powers

A. Kumchev (1999)

Acta Arithmetica

A Diophantine inequality with four squares and one $k$ th power of primes

Quanwu Mu, Minhui Zhu, Ping Li (2019)

Czechoslovak Mathematical Journal

Let $k \geq 5$ be an odd integer and $η$ be any given real number. We prove that if $λ_{1}$ , $λ_{2}$ , $λ_{3}$ , $λ_{4}$ , $μ$ are nonzero real numbers, not all of the same sign, and $λ_{1} / λ_{2}$ is irrational, then for any real number $σ$ with $0 < σ < 1 / (8 ϑ (k))$ , the inequality $| λ_{1} p_{1}^{2} + λ_{2} p_{2}^{2} + λ_{3} p_{3}^{2} + λ_{4} p_{4}^{2} + μ p_{5}^{k} + η | < {(max_{1 \leq j \leq 5} p_{j})}^{- σ}$ has infinitely many solutions in prime variables $p_{1}, p_{2}, \dots, p_{5}$ , where $ϑ (k) = 3 \times 2^{(k - 5) / 2}$ for $k = 5, 7, 9$ and $ϑ (k) = [(k^{2} + 2 k + 5) / 8]$ for odd integer $k$ with $k \geq 11$ . This improves a recent result in W. Ge, T. Wang (2018).

A hybrid of theorems of Goldbach and Piatetski-Shapiro

Hongze Li (2003)

Acta Arithmetica

A new form of the circle method, and its application to quadratic forms.

D.R. Heath-Brown (1996)

Journal für die reine und angewandte Mathematik

A new upper bound for Waring's problem (mod p)

J. Bovey (1977)

Acta Arithmetica

A Note on the Exceptional Set for Goldbach's Problem in Short Intervals.

A. Perelli, J. Pintz, J. Kaczorowski (1993)

Monatshefte für Mathematik

A numerical bound for small prime solutions of some ternary linear equations

Ming-Chit Liu, Tianze Wang (1998)

Acta Arithmetica

A propos du problème de Waring

Jean-Marc DESHOUILLERS (1971/1972)

Seminaire de Théorie des Nombres de Bordeaux

A reduction technique in Waring's problem, I

Kent D. Boklan (1993)

Acta Arithmetica

A short intervals result for linear equations in two prime variables.

M. B. S. Laporta (1997)

Revista Matemática de la Universidad Complutense de Madrid

Given A and B integers relatively prime, we prove that almost all integers n in an interval of the form [N, N+H], where N exp(1/3+e) ≤ H ≤ N can be written as a sum Ap1 + Bp2 = n, with p1 and p2 primes and e an arbitrary positive constant. This generalizes the results of Perelli et al. (1985) established in the classical case A=B=1 (Goldbach's problem).

A sieve approach to the Waring-Goldbach problem. I. Sums of four cubes

Jörg Brüdern (1995)

Annales scientifiques de l'École Normale Supérieure

A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem

Jörg Brüdern (1995)

Acta Arithmetica

A ternary Diophantine inequality over primes

Roger Baker, Andreas Weingartner (2014)

Acta Arithmetica

Let 1 < c < 10/9. For large real numbers R > 0, and a small constant η > 0, the inequality $| p ₁^{c} + p ₂^{c} + p ₃^{c} - R | < R^{- η}$ holds for many prime triples. This improves work of Kumchev [Acta Arith. 89 (1999)].

Currently displaying 1 – 20 of 32

Page 1 Next

Displaying 1 – 20 of 32

A Bound for Prime Solutions of Some Ternary Equations.

A diophantine inequality involving prime powers

A Diophantine inequality with four squares and one $k$ th power of primes

A hybrid of theorems of Goldbach and Piatetski-Shapiro

A new form of the circle method, and its application to quadratic forms.

A new upper bound for Waring's problem (mod p)

A Note on the Exceptional Set for Goldbach's Problem in Short Intervals.

A numerical bound for small prime solutions of some ternary linear equations

A propos du problème de Waring

A reduction technique in Waring's problem, I

A short intervals result for linear equations in two prime variables.

A sieve approach to the Waring-Goldbach problem. I. Sums of four cubes

A sieve approach to the Waring-Goldbach problem, II On the seven cubes theorem

A ternary Diophantine inequality over primes

Addendum and corrigendum to the paper "On sums of powers and a related problem", Acta Arith. 36 (1980), pp. 125-141

Additive inhomogeneous Diophantine inequalities

Additive problems with prime numbers of special type

Additive representation in thin sequences, I : Waring's problem for cubes

Additive representation in thin sequences, III: asymptotic formulae

An additive divisor problem.

Currently displaying 1 – 20 of 32