Results 81 to 90 of about 1,648,333 (245)
An elegant model of the geodesic flow on the modular surface
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Caroline Series' [The modular surface and continued fractions, J. Lond. Math. Soc. (2), 31, no. 1, (1985), 69–80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well‐chosen symbolic coding.
Pierre Arnoux, Thomas A. Schmidt
wiley +1 more source
Fibonacci and Lucas numbers close to Narayana's cows numbers
Researches in MathematicsIn this study, we find all Fibonacci and Lucas numbers which are close to Narayana's cows numbers. The main tools used in this work are lower bounds for linear forms in logarithms due to Matveev and Dujella-Pethö version of the Baker-Davenport reduction ...
A. Satapathy +3 more
doaj +1 more source
TRANSFERENCE THEOREMS FOR DIOPHANTINE APPROXIMATION WITH WEIGHTS [PDF]
Mathematika, 2019 In this paper we prove transference inequalities for regular and uniform Diophantine exponents in the weighted setting. Our results generalize the corresponding inequalities that exist in the `non-weighted' case.
O. German
semanticscholar +1 more source
Definability of complex functions in o‐minimal structures
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract We prove that holomorphic continuations of functions in the classes an∗$\mathbf {an}^*$ and G$\mathcal {G}$ are definable in the o‐minimal structures Ran∗$\mathbb {R}_{\operatorname{an}^*}$ and RG$\mathbb {R}_{\mathcal {G}}$, respectively. More specifically, we give complex domains on which the holomorphic continuations are definable and show ...
Adele Padgett, Patrick Speissegger
wiley +1 more source
A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation [PDF]
, 2017 We establish a new connection between metric Diophantine approximation and the parametric geometry of numbers by proving a variational principle facilitating the computation of the Hausdorff and packing dimensions of many sets of interest in Diophantine ...
Tushar Das +3 more
semanticscholar +1 more source
Higher-rank Bohr sets and multiplicative diophantine approximation [PDF]
Compositio Mathematica, 2018 Gallagher’s theorem is a sharpening and extension of the Littlewood conjecture that holds for almost all tuples of real numbers. We provide a fibre refinement, solving a problem posed by Beresnevich, Haynes and Velani in 2015.
Sam Chow, Niclas Technau
semanticscholar +1 more source
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
Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley +1 more source
New Hardness Results for Diophantine Approximation [PDF]
We revisit simultaneous diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input of the decision version of this problem consists of a rational vector \alpha, an error
Rothvoß, Thomas, Eisenbrand, Friedrich
core +2 more sources
Estimates for diophantine approximation constants [PDF]
, 1980 It is proved that the three-dimensional Diophantine approximation constant is at least 2(275)−12.
Cusick, T.W.
core +1 more source