Results 61 to 70 of about 476,689 (165)
Exact local distribution of the absolutely continuous spectral measure
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract It is well‐established that the spectral measure for one‐frequency Schrödinger operators with Diophantine frequencies exhibits optimal 1/2$1/2$‐Hölder continuity within the absolutely continuous spectrum (Avila and Jitomirskaya, Commun. Math. Phys. 301 (2011), 563–581).
Xianzhe Li, Jiangong You, Qi Zhou
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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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Transference inequalities for multiplicative diophantine exponents [PDF]
Proceedings of the Steklov Institute of Mathematics, 2011 In this paper we prove inequalities for multiplicative analogues of Diophantine exponents, similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly approximable and establish some inequalities connecting multiplicative exponents with ordinary ones.
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A New Diophantine Approximation Inequality on Surfaces and Its Applications [PDF]
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context.
Xiao, Zheng, Levin, Aaron, Huang, Keping
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Volumes and diophantine inequalities associated with decomposable forms [PDF]
, 2003 For homogeneous decomposable forms F(X) in n variables with real coefficients, we consider the associated volume of all real solutions x∈Rn to the inequality |F(x)|⩽1. We relate this to the number of integral solutions z∈Zn to the Diophantine inequality |
Thunder, Jeffrey Lin
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Diophantine Equation in Logarithms [PDF]
, 2023 The main work of these pages is written by myself under the supervisor of Dr. Omar Kihel, pertaining to continued fractions and applications , linear form in logarithms and the solutions of Diophantine equation Fn1 + Fn2 + Fn3 + Fn4 = 6a .
Tian, Zhao
core
Diophantine equations involving factorials [PDF]
, 2017 summary:We study the Diophantine equations $(k!)^n -k^n = (n!)^k-n^k$ and $(k!)^n +k^n = (n!)^k +n^k,$ where $k$ and $n$ are positive integers. We show that the first one holds if and only if $k=n$ or $(k,n)=(1,2),(2,1)$ and that the second one holds if ...
Luca, Florian, Alzer, Horst
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Diophantine inequalities with mixed powers, II
Journal of Number Theory, 1979 AbstractIt is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at least one of the ratios λiλj (1 ≤ j ≤ 3) is irrational then the values taken by λ1x12 + λ2x22 + λ3x32 + λ4x43 + λ5x53 for integer values of x1, …, x5 are everywhere dense on the real line.
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Perfect Powers in Smarandache Type Expressions [PDF]
, 2004 The author showed that there are only finitely many numbers of the above form which are products of ...
Luca, Florian
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On a variant of Pillai's problem involving <i>S</i>-units and Fibonacci numbers. [PDF]
Bol Soc Mat Mex, 2022 Ziegler V.
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