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Subjects
11-XX Number theory
11Pxx Additive number theory; partitions
11P55 Applications of the Hardy-Littlewood method

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Displaying 81 – 100 of 187

On a Diophantine problem with two primes and s powers of two

Alessandro Languasco, Alessandro Zaccagnini (2010)

Acta Arithmetica

On a problem of sums of mixed powers

Ming Lu (1991)

Acta Arithmetica

On a problem of the Additive Theory of Numbers

C.J.A. and E.H. Linfoot Franklin (1929)

Mathematische Zeitschrift

On a ternary Diophantine problem with mixed powers of primes

Alessandro Languasco, Alessandro Zaccagnini (2013)

Acta Arithmetica

Let 1 < k < 33/29. We prove that if λ₁, λ₂ and λ₃ are non-zero real numbers, not all of the same sign and such that λ₁/λ₂ is irrational, and ϖ is any real number, then for any ε > 0 the inequality $| λ ₁ p ₁ + λ ₂ p ² ₂ + λ ₃ p ₃^{k} + ϖ | \leq {(m a x_{j} p_{j})}^{- (33 - 29 k) / (72 k) + ε}$ has infinitely many solutions in prime variables p₁, p₂, p₃.

On an additive problem of unlike powers in short intervals

Qingqing Zhang (2022)

Czechoslovak Mathematical Journal

We prove that almost all positive even integers $n$ can be represented as $p_{2}^{2} + p_{3}^{3} + p_{4}^{4} + p_{5}^{5}$ with $| p_{k}^{k} - \frac{1}{4} N | \leq N^{1 - 1 / 54 + ε}$ for $2 \leq k \leq 5$ . As a consequence, we show that each sufficiently large odd integer $N$ can be written as $p_{1} + p_{2}^{2} + p_{3}^{3} + p_{4}^{4} + p_{5}^{5}$ with $| p_{k}^{k} - \frac{1}{5} N | \leq N^{1 - 1 / 54 + ε}$ for $1 \leq k \leq 5$ .

On certain additive representations of integers

Thanigasalam, K. (1983/1984)

Portugaliae mathematica

On divisors of sums of integers. II.

A. Sárközy, C.L. Stewart (1986)

Journal für die reine und angewandte Mathematik

On Generalized Quadratic Equations in Three Prime Variables.

Ming-Chit Liu, Man-Cheung Leung (1993)

Monatshefte für Mathematik

On indefinite diagonal forms in many variables.

Hans Peter Schlickewei (1979)

Journal für die reine und angewandte Mathematik

On Linnik's approximation to Goldbach's problem, I

J. Pintz, I. Z. Ruzsa (2003)

Acta Arithmetica

On nonary cubic forms.

Christopher Hooley (1988)

Journal für die reine und angewandte Mathematik

On nonary cubic forms: II.

Christopher Hooley (1991)

Journal für die reine und angewandte Mathematik

On nonary cubic forms: III.

Christopher Hooley (1994)

Journal für die reine und angewandte Mathematik

On pairs of Goldbach-Linnik equations with unequal powers of primes

Enxun Huang (2023)

Czechoslovak Mathematical Journal

It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.

On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II

R. Nair (1993)

Studia Mathematica

On sets of polynomials whose difference set contains no squares

Thái Hoàng Lê, Yu-Ru Liu (2013)

Acta Arithmetica

Let $_{q} [t]$ be the polynomial ring over the finite field $_{q}$ , and let $_{N}$ be the subset of $_{q} [t]$ containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set $A \subseteq_{N}$ for which A-A contains no squares of polynomials. By combining the polynomial Hardy-Littlewood circle method with the density increment technology developed by Pintz, Steiger and Szemerédi, we prove that $D (N) ≪ q^{N} {(l o g N)}^{7} / N$ .

On simultaneous additive equations II.

Trevor D. Wooley (1991)

Journal für die reine und angewandte Mathematik

On simultaneous diagonal equations and inequalities

J. Brüdern, R. J. Cook (1992)

Acta Arithmetica

On sums of five almost equal prime squares

Jianya Liu, Tao Zhan (1996)

Acta Arithmetica

On sums of powers and a related problem

K. Thanigasalam (1980)

Acta Arithmetica

Currently displaying 81 – 100 of 187

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