Results 61 to 70 of about 11,736 (207)
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
Physica A: Statistical Mechanics and its Applications, 2008 We introduce a new class of deterministic networks by associating networks with Diophantine equations, thus relating network topology to algebraic properties. The network is formed by representing integers as vertices and by drawing cliques between M vertices every time that M distinct integers satisfy the equation.
Bedogne, C, Masucci, AP, Rodgers, GJ
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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
Linear Diophantine Fuzzy Rough Sets on Paired Universes with Multi Stage Decision Analysis
Axioms, 2022 Rough set (RS) and fuzzy set (FS) theories were developed to account for ambiguity in the data processing. The most persuasive and modernist abstraction of an FS is the linear Diophantine FS (LD-FS).
Saba Ayub +5 more
doaj +1 more source
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 +2 more
wiley +1 more source
Journal of MathematicsSolving the Diophantine equation has fascinated mathematicians from various civilizations. In this paper, we propose the resolution of quadratic Diophantine equations with integer coefficients.
Francklin Fenolahy +2 more
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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
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, 2019 In this paper we find a parametric solution to the hitherto unsolved problem of finding three positive integers such that their sum, the sum of their squares and the sum of their cubes are simultaneously perfect squares.
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Strong Diophantine Triples [PDF]
Experimental Mathematics, 2008 We prove that there exist infinitely many triples a, b, c of non-zero rationals with the property that a^2 + 1, b^2 + 1, c^2 + 1, ab + 1, ac + 1 and bc + 1 are perfect squares.
Andrej Dujella, Vinko Petriccevic
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Three Diophantine equations concerning the polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsMany 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
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