Results 71 to 80 of about 1,143,114 (202)

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

Diophantine equations

, 2023
U radu je opisan pojam diofantskih jednadžbi. Dan je kratki povijesni pregled, te upoznavanje s Diofantom Aleksandrijskim koji je zaslužan za ovo polje matematike. Detaljno su opisane vrste diofantskih jednadžbi te metode njihovog rješavanja.
Plosnić, Josip Daniel
core   +2 more sources

On the exceptional set in Littlewood's discrete conjecture

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
wiley   +1 more source

Multiplicative Diophantine equations

Journal of Number Theory, 1992
The solution of the diophantine equation \(\prod_{i=1}^ n x_ i= \prod_{i=1}^ n y_ i\) is given in terms of \(n^ 2\) parameters (Bell's theorem) [cf. the first author, Proc. Ramanujan Cent. Int. Conf., Annamalainagar/India 1987, RMS Publ. 1, 141-146 (1988; Zbl 0696.10014)].
Srinivasa Rao, K., Santhanam, T.S., Rajeswari, V.   +2 more
openaire   +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

On a few Diophantine equations, in particular, Fermat's last theorem

International Journal of Mathematics and Mathematical Sciences, 2003
This is a survey on Diophantine equations, with the purpose being to give the flavour of some known results on the subject and to describe a few open problems.
C. Levesque
doaj   +1 more source

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

On some diophantine equations involving factorials [PDF]

Mathematica Bohemica
We study the Diophantine equations $(n!)^k - n^k = (k!)^n - k^n$ and $(n!)^k + n^k = (k!)^n + k^n$, where $k$ and $n$ are positive integers. According to H. Arzel, F. Luca (2017), only the first equation has nontrivial solutions. It is proved also that ${
Maciej Gnatowski
doaj   +1 more source

HNN extensions and embedding theorems for groups

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract The Higman–Neumann–Neumann (HNN) paper of 1949 is a landmark of group theory in the 20th century. The proof of its main theorem covers less than a page and uses only pre‐existing technology, but the construction that it introduced, the HNN extension, quickly became one of the principal tools of combinatorial group theory, widely used to build ...
Martin R. Bridson, Carl‐Fredrik Nyberg‐Brodda   +1 more
wiley   +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