Results 61 to 70 of about 304 (165)
Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
wiley +1 more source
Counting intrinsic Diophantine approximations in simple algebraic groups
, 2021 We establish an explicit asymptotic formula for the number of rational solutions of intrinsic Diophantine inequalities on simply-connected simple algebraic groups, at arbitrarily small ...
Nevo, Amos, Ghosh, Anish, Gorodnik, Alex
core
Analytic Methods for Diophantine Equations and Diophantine Inequalities
, 2005 Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities.
H. Davenport, T. D. Browning
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A theorem in diophantine approximations
, 1973 In this paper we derive, under certain conditions, an asymptotic formula for the number of solutions of diophantine inequalities involving systems of linear ...
Melvin M Sweet, Sweet, Melvin M
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On a general Diophantine inequality
Functiones et Approximatio Commentarii Mathematici, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ADDITIVE REPRESENTATION IN THIN SEQUENCES, VIII: DIOPHANTINE INEQUALITIES IN REVIEW
, 2010 Recent developments in the theory of diophantine inequalities and the Davenport-Heilbronn method are discussed and then directed toward specific inequalities of definite character. Special emphasis is on the value-distribution of diagonal forms near thin
Wooley, Trevor D. +2 more
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Diophantine inequalities for ternary diagonal forms
, 2018 We discuss small solutions to ternary diagonal inequalities of any degree where all of the variables are assumed to be of size P. We study this problem on average over a one-parameter family of forms and discuss a generalization of work of Bourgain on ...
Schindler, Damaris
core
Diophantine inequalities with mixed powers
, 1977 It is shown that λ1, λ2,…, λ6, μ are not all of the same sign and at least one ratio λiλj is irrational then the values taken by λ1x13 + ⋯ + λ6x63 + μy3 for integer values of x1 ,…, x6, y are everywhere dense on the real line.
Cook, P.J.
core +1 more source
Characterizing the sum of two cubes
, 2003 An intrinsic characterization of positive integers which can be represented as the sum or difference of two cubes is given. Every integer has a smallest multiple with is a sum of two cubes and such that the multiple, in the form of an iterated function ...
Kevin A. Broughan, Broughan, Kevin A.
core
Analytic methods for Diophantine equations and Diophantine inequalities, by Harold Davenport
, 2005 Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to ...
Browning, TD
core