Results 101 to 110 of about 2,483 (259)

DIOPHANTINE APPROXIMATION BY PRIMES [PDF]

Glasgow Mathematical Journal, 2009
AbstractWe show that whenever δ > 0 and constants λisatisfy some necessary conditions, there are infinitely many prime triplesp1,p2,p3satisfying the inequality |λ0+ λ1p1+ λ2p2+ λ3p3| < (maxpj)−2/9+δ. The proof uses Davenport–Heilbronn adaption of the circle method together with a vector sieve method.
openaire   +1 more source

Padé approximations and diophantine geometry [PDF]

Proceedings of the National Academy of Sciences, 1985
Using methods of Padé approximations we prove a converse to Eisenstein's theorem on the boundedness of denominators of coefficients in the expansion of an algebraic function, for classes of functions, parametrized by meromorphic functions. This result is applied to the Tate conjecture on the effective description of isogenies for elliptic curves.
Chudnovsky, D. V., Chudnovsky, G. V.
openaire   +2 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

Padé Approximations and Irrationality Measures on Values of Confluent Hypergeometric Functions

Mathematics
Padé approximations are approximations of holomorphic functions by rational functions. The application of Padé approximations to Diophantine approximations has a long history dating back to Hermite. In this paper, we use the Maier–Chudnovsky construction
Jiaxin Hu, Chenglong Yu, Kangyun Zhou
doaj   +1 more source

A Diophantine approximation problem with two primes and one k-th power of a prime [PDF]

Journal of Number Theory, 2017
We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a $k$-th power of a prime which was only proved to hold for ...
Alessandro Gambini, A. Languasco, A. Zaccagnini   +2 more
semanticscholar   +1 more source

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

Diophantine Approximation of Matrices

Rocky Mountain Journal of Mathematics, 1996
Bezeichnet \(M(\ell,m;K)\) die Menge der \(\ell\times m\)-Matrizen über einem Ring \(K\), so wird in der vorliegenden Arbeit die Approximation von \(B\in M(\ell,m;\mathbb{R})\) durch Matrizen \(P\in M(\ell,m;\mathbb{Z})\) untersucht. Im ersten Teil beschäftigen sich die Autoren mit oberen, im zweiten mit unteren Schranken für \(|B|:=\min\{|B-P|: P\in M(
Have, G.N. ten, Tijdeman, R.
openaire   +2 more sources

An equivalence principle between polynomial and simultaneous Diophantine approximation [PDF]

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2017
We show that Mahler's classification of real numbers $\zeta$ with respect to the growth of the sequence $(w_{n}(\zeta))_{n\geq 1}$ is equivalently induced by certain natural assumptions on the decay of the sequence $(\lambda_{n}(\zeta))_{n\geq 1 ...
J. Schleischitz
semanticscholar   +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

Diophantine approximation on lines with prime constraints

, 2014
We study the problem of Diophantine approximation on lines in R2 with prime numerator and ...
Ghosh, A., Baier, S.
core   +1 more source