Results 41 to 50 of about 312 (173)

Exponential and sub-exponential stability times for the NLS on the circle [PDF]

, 2019
In this note we study stability times for a family of parameter dependent nonlinear Schrodinger equations on the circle, close to the origin. Imposing a suitable Diophantine condition (first introduced by Bourgain), we state a rather flexible Birkhoff ...
Procesi, M., Biasco, L., Massetti, J. E.
core   +4 more sources

Moderate Deviation Principles for Lacunary Trigonometric Sums

Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.
ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley   +1 more source

Ternary Diophantine Equations via Galois Representations and Modular Forms [PDF]

, 2004
In this paper, we develop techniques for solving ternary Diophantine equations of the shape Axn + Byn = Cz2, based upon the theory of Galois representations and modular forms.
Michael A. Bennett, Chris M. Skinner
core   +1 more source

Double‐jump phase transition for the reverse Littlewood–Offord problem

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract Erdős conjectured in 1945 that for any unit vectors v1,…,vn$v_1, \ldots, v_n$ in R2$\mathbb {R}^2$ and signs ε1,…,εn$\varepsilon _1, \ldots, \varepsilon _n$ taken independently and uniformly in {−1,1}$\lbrace -1,1\rbrace$, the random Rademacher sum σ=ε1v1+⋯+εnvn$\sigma = \varepsilon _1 v_1 + \cdots + \varepsilon _n v_n$ satisfies ∥σ∥2⩽1$\Vert \
Lawrence Hollom, Julien Portier, Victor Souza   +2 more
wiley   +1 more source

Some exponential diophantine equations [PDF]

, 2013
Thesis (MSc)--Stellenbosch University, 2013.ENGLISH ABSTRACT: The aim of this thesis is to study some methods used in solving exponential Diophan- tine equations.
Mabaso, Automan Sibusiso
core  

Sums of three positive cubes

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
wiley   +1 more source

Curious Continued Fractions, Nonlinear Recurrences and Transcendental Numbers [PDF]

, 2015
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear ...
Hone, Andrew N.W.
core  

Polynomial–exponential equations and Zilber's conjecture [PDF]

, 2016
Assuming Schanuel's conjecture, we prove that any polynomial–exponential equation in one variable must have a solution that is transcendental over a given finitely generated field.
Mantova, V, Zannier, U
core   +1 more source

Random Diophantine equations in the primes II

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract Let d⩾2$d\geqslant 2$ and n⩾d$n\geqslant d$ with (d,n)∉{(2,2),(3,3)}$(d,n)\notin \lbrace (2,2),(3,3)\rbrace$. We consider homogeneous Diophantine equations of degree d$d$ in n+1$n+1$ variables and whether they have solutions in the primes.
Philippa Holdridge
wiley   +1 more source

Powers in the Lucas sequence when the index is divisible by three [PDF]

, 2011
In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are ...
Rodrigo Hitos, Javier, López González, M. Dolores   +1 more
core   +1 more source