Results 1 to 10 of about 55 (52)

The Davenport–Heilbronn method: 80 years on

Journal of the London Mathematical Society
Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc . (1) 21 (1946), 185–193). We discuss the main
Tim Browning
openaire   +3 more sources

Diophantine approximation with one prime, two squares of primes and one kth power of a prime

Open Mathematics, 2021
Let ...
Gambini Alessandro
doaj   +1 more source

The integral part of a nonlinear form with a square, a cube and a biquadrate

Open Mathematics, 2020
In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
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One Diophantine inequality with unlike powers of prime variables

Journal of Inequalities and Applications, 2016
In this paper, we show that if λ 1 $\lambda_{1}$ , λ 2 $\lambda_{2}$ , λ 3 $\lambda_{3}$ , λ 4 $\lambda _{4}$ , λ 5 $\lambda_{5}$ are nonzero real numbers not all of the same sign, η is real, 0 < σ < 1 720 ...
Wenxu Ge, Weiping Li
doaj   +1 more source

A note on Diophantine inequalities in function fields [PDF]

Notes on Number Theory and Discrete Mathematics
We will discuss how the Bentkus–Götze–Freeman variant of the Davenport–Heilbronn circle method can be used to study 𝔽_q[t] solutions to inequalities of the form ord(λ₁p₁ᵏ+...+λₛpₛᵏ-γ)
Kathryn Wilson
doaj   +1 more source

On the asymptotic formula in Waring's problem with shifts [PDF]

, 2018
We show that for integers k≥4 and s≥k2+(3k−1)/4, we have an asymptotic formula for the number of solutions to the inequality |(x1−θ1)k+…+(xs−θs)k−τ|<η in positive integers xi, where θi∈(0,1) with θ1 irrational, η∈(0,1], and τ>0 is sufficiently ...
Biggs, Kirsti D., Kirsti D. Biggs
core   +1 more source

On Diophantine approximation by unlike powers of primes

Open Mathematics, 2019
Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irrational, λ2/λ4 and λ3/λ5 are rational. Let η real, and ε > 0.
Ge Wenxu, Li Weiping, Wang Tianze
doaj   +1 more source

CUBIC DIOPHANTINE INEQUALITIES INVOLVING A NORM FORM

, 2011
We apply Freeman's variant of the Davenport–Heilbronn method to provide an asymptotic formula for the number of small values taken by a certain family of cubic forms with real coefficients. The cubic forms in question arise as the sum of a diagonal form
M. P. HARVEY
core   +1 more source

Exceptional Sets for Diophantine Inequalities

, 2014
We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument.
Wooley, Trevor D., Parsell, Scott T.
core   +1 more source