Results 51 to 60 of about 2,597 (231)

Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems

Annalen der Physik, Volume 538, Issue 7, July 2026.
ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández, Daniel Gutiérrez‐Ruiz, Diego Gonzalez, J. David Vergara   +3 more
wiley   +1 more source

ON A DIOPHANTINE EQUATION OF CASSELS [PDF]

Glasgow Mathematical Journal, 2005
In 1985 J.W.S. Cassels solved the problem of determening all the triples of consecutive cubes whose sum is a square, \textit{i.e.} he solved completely the elliptic Diophantine equation \(\,y^2=3x(x^2+2)\) (the solutions for \(x\) are \(0\), \(1\), \(2\) and \(24\)).
Luca, F., Walsh, P. G.
openaire   +2 more sources

Three Diophantine equations concerning the polygonal numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Many authors investigated the problem about the linear combination of two polygonal numbers being a perfect square, i.e., the Diophantine equation mPₖ(x)+nPₖ(y)=z², where Pₖ(x) denotes the x-th k-polygonal number and m, n are positive integers.
Yong Zhang, Mei Jiang, Qiongzhi Tang
doaj   +1 more source

On the moments of exponential sums over r$r$‐free polynomials

Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.
Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
wiley   +1 more source

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

On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n [PDF]

, 2010
In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers.
Farzaneh , A., Mahmoudvand , R., Hassani, Hossein, Howell, G.   +3 more
core  

Multiplicatively dependent integer vectors on a hyperplane

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman, Valentio Iverson, Gian Cordana Sanjaya   +2 more
wiley   +1 more source

Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences [PDF]

, 2008
Somos 4 sequences are a family of sequences defined by a fourth-order quadratic recurrence relation with constant coefficients. For particular choices of the coefficients and the four initial data, such recurrences can yield sequences of integers.
Swart, Christine, Hone, Andrew N.W.
core   +1 more source

Application of the group action approach to solving linear Diophantine equations [PDF]

Известия Саратовского университета. Новая серия: Математика. Механика. Информатика
The article substantiates a method for solving linear Diophantine equations using the theory of group actions. The purpose of this paper is to introduce actions of certain groups on the set of linear Diophantine equations and to study their ...
Chistov, Ivan Sergeevich, Tsybulya, Liliya Mikhailovna   +1 more
doaj   +1 more source

On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.
Alan Murat
doaj   +1 more source