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Exceptional Sets for Diophantine Inequalities [PDF]

International Mathematics Research Notices, 2012
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.
S. Parsell, T. Wooley
semanticscholar   +10 more sources

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   +3 more sources

DIOPHANTINE INEQUALITIES OF FRACTIONAL DEGREE [PDF]

Mathematika, 2021
This paper is concerned with the study of diagonal Diophantine inequalities of fractional degree θ, where θ > 2 is real and non-integral. For fixed non-zero real numbers λi not all of the same sign we write F(x) = λ1x θ 1 + · · ·+ λsx θ s .
C. Poulias
semanticscholar   +6 more sources

Gowers norms control diophantine inequalities [PDF]

Algebra & Number Theory, 2017
A central tool in the study of systems of linear equations with integer coefficients is the Generalised von Neumann Theorem of Green and Tao. This theorem reduces the task of counting the weighted solutions of these equations to that of counting the ...
A. Walker
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A note on some Diophantine inequalities over adelic curves [PDF]

Journal de Théorie des Nombres de Bordeaux, 2023
Without assuming the Northcott property we provide an upper bound on the number of “big solutions” of a special system of Diophantine inequalities over proper adelic curves.
Paolo Dolce
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A System of Two Diophantine Inequalities with Primes

Journal of Mathematics, 2021
Let ...
Xue Han, Huafeng Liu, Deyu Zhang
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On two Diophantine inequalities over primes [PDF]

Indagationes Mathematicae, 2016
21 ...
Min Zhang, Jinjia Li
semanticscholar   +7 more sources

Some Diophantine equations and inequalities with primes [PDF]

, 2020
The inequalities concern the sum of s powers of primes with non-integer exponent c>1. Here s =2,3,4,or 5. The equations are similar, taking integer part before summing; here s = 3 or 5.
R. Baker
semanticscholar   +3 more sources

LINEAR DIOPHANTINE INEQUALITIES APPLIED TO GENERALIZED FABER POLYNOMIALS. [PDF]

Proc Natl Acad Sci U S A, 1960
Motzkin TS.
europepmc   +3 more sources

On Some Diophantine Inequalities Involving the Exponential Function [PDF]

Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 1965
Alan R. H. Baker
semanticscholar   +2 more sources