Results 61 to 70 of about 446 (186)
Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In 2019 Kleinbock and Wadleigh proved a “zero‐one law” for uniform inhomogeneous Diophantine approximations. We generalize this statement to arbitrary weight functions and establish a new and simple proof of this statement, based on the transference principle. We also give a complete description of the sets of g$g$‐Dirichlet pairs with a fixed
Vasiliy Neckrasov
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Diophantine equations in partitions [PDF]
Mathematics of Computation, 1984 Given positive integers r 1
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Distribution of integer points on determinant surfaces and a mod‐p analogue
Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
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f$f$‐Diophantine sets over finite fields via quasi‐random hypergraphs from multivariate polynomials
Mathematika, Volume 72, Issue 2, April 2026.Abstract We investigate f$f$‐Diophantine sets over finite fields via new explicit constructions of families of quasi‐random hypergraphs from multivariate polynomials. In particular, our construction not only offers a systematic method for constructing quasi‐random hypergraphs but also provides a unified framework for studying various hypergraphs ...
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
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An exponential diophantine equation [PDF]
Bulletin of the Australian Mathematical Society, 2001 Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.
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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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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
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Symmetric Diophantine Equations
Rocky Mountain Journal of Mathematics, 2004 The author describes a method to obtain infinite parametric solutions of some Diophantine equations of type \(f(x,y)=f(u,v)\) where \(f\) is a form (usually the product of some linear and quadratic forms) with rational coefficients. The main idea is to apply a non-singular linear transformation \(x=\alpha u+\beta v\), \(y=\gamma u+\delta v\) such that ...
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Journal of Geophysical Research: Space Physics, Volume 131, Issue 3, March 2026.Abstract The wave telescope is an analysis technique for multi‐point spacecraft data that estimates power spectra in reciprocal position space (k $k$‐space). It has been used to reveal the spatial properties of waves and fluctuations in space plasmas. Originally designed as an analysis tool for 4 spacecraft constellations, new multi‐scale missions such
L. Schulz +7 more
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