Results 41 to 50 of about 321 (189)

On some exponential diophantine equations [PDF]

, 2019
Anadolu Üniversitesi ve Bilecik Şeyh Edebali Üniversitesi tarafından ortak yürütülen program.Üç bölümden oluşan bu çalışmada sayılar teorisinin insanlık tarihi kadar eski sayılabilecek problemlerinden birisi olan Diophantine denklemlerinin özel bir ...
Akkuş, Seda Nur
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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
wiley   +1 more source

On the exponential diophantine equations of degree three [PDF]

, 2019
Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper concentrates on finding an integral solution to the exponential Diophantine equation of degree three.
Sapar, Siti Hasana, Amalul Hair, Nur Hidayah   +1 more
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Heights and multiplicative relations on algebraic varieties [PDF]

, 2007
Points on a subvariety X of a semi-abelian variety A that are contained in a subgroup, let the subgroup be of finite rank or algebraic, are subject to severe restrictions arithmetical nature. Finiteness results for intersections of X with subgroups of
Habegger, Philipp
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New results on embeddings of self‐similar sets via renormalization

Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.
Abstract For self‐similar sets X,Y⊆R$X,Y\subseteq \mathbb {R}$, we obtain new results toward the affine embeddings conjecture of Feng–Huang–Rao (2014), and the equivalent weak intersections conjecture. We show that the conjecture holds when the defining maps of X,Y$X,Y$ have algebraic contraction ratios, and also for arbitrary Y$Y$ when the maps ...
Amir Algom, Michael Hochman, Meng Wu
wiley   +1 more source

Powers in the Lucas sequence when the index is divisible by three [PDF]

, 2011
In this paper the m-powers with m ≥ 2 included in the Lucas sequences when the index satisfies some conditions are ...
Rodrigo Hitos, Javier, López González, M. Dolores   +1 more
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Classical and modular approaches to exponential Diophantine equations - II. The Lebesgue-Nagell equation [PDF]

, 2006
This is the second in a series of papers where we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat's Last ...
Mignotte, Maurice, Bugeaud, Yann, Siksek, Samir   +2 more
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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

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

On the Exponential Diophantine Equation 7^x − 5^y = z^2 [PDF]

In this paper, we address the exponential Diophantine equation 7x − 5y = z2 , seeking non-negative integer solutions for x, y, and z. Using many congruence theorems and Catalan’s conjecture, we prove the existence of a single solution. Our analysis shows
BUDEE U ZAMAN
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