Results 21 to 30 of about 3,220 (237)
On Joint Universality in the Selberg–Steuding Class
Mathematics, 2023 The famous Selberg class is defined axiomatically and consists of Dirichlet series satisfying four axioms (Ramanujan hypothesis, analytic continuation, functional equation, multiplicativity).
Roma Kačinskaitė +2 more
doaj +1 more source
Linear forms in two logarithms and Schneider's method. II [PDF]
Acta Arithmetica, 1989 Verf. verfeinern ihre in [Acta Arith. 53, No.3, 251-287 (1989; Zbl 0642.10034)] erhaltene untere Abschätzung für \(| b_ 1 \log \alpha_ 1-b_ 2 \log \alpha_ 2| \neq 0\) bei algebraischen \(\alpha_ j\neq 0\) und ganzrationalen \(b_ j\). Dazu kombinieren sie ihre a.a.O. entwickelte Methode mit einer Technik, die sie bereits in [Math. Ann.
Mignotte, Maurice, Waldschmidt, Michel
openaire +2 more sources
Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt
Journal of Mathematics, 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br=Js+Jt and Cr=Js+Jt are completely solved.
Ahmed Gaber, Mohiedeen Ahmed
doaj +1 more source
The extensibility of the Diophantine triple {2, b, c}
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple.
Adžaga Nikola +2 more
doaj +1 more source
Padovan and Perrin numbers of the form 7ᵗ-5ᶻ-3ʸ-2ˣ [PDF]
Notes on Number Theory and Discrete MathematicsConsider the Padovan sequence (pₙ)ₙ≥₀ given by pₙ₊₃=pₙ₊₁+pₙ with p₀=p₁=p₂=1. Its companion sequence, the Perrin sequence (℘ₙ)ₙ≥₀, follows the same recursive formula as the Padovan numbers, but with different initial values: p₀=3, p₁=0 and p₂=2.
Djamel Bellaouar +2 more
doaj +1 more source
Common values of two k-generalized Pell sequences [PDF]
Notes on Number Theory and Discrete MathematicsLet k≥2 and let (Pₙ⁽ᵏ⁾)ₙ≥₂₋ₖ be the k-generalized Pell sequence defined by Pₙ⁽ᵏ⁾=2Pₙ₋₁⁽ᵏ⁾+2Pₙ₋₂⁽ᵏ⁾+...+2Pₙ₋ₖ⁽ᵏ⁾ for n≥2 with initial conditions P₋₍ₖ₋₂₎⁽ᵏ⁾=P₋₍ₖ₋₃₎⁽ᵏ⁾=...=P₋₁⁽ᵏ⁾=P₀⁽ᵏ⁾=0, and P₁⁽ᵏ⁾=1.
Zafer Şiar +2 more
doaj +1 more source
A kit for linear forms in three logarithms
Mathematics of Computation, 2023 We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds for linear forms in logarithms.
Mignotte, Maurice, Voutier, Paul
openaire +2 more sources
A p-adic lower bound for a linear form in logarithms
International Journal of Number Theory, 2022 Linear forms in logarithms have an important role in the theory of Diophantine equations. In this paper, we prove explicit [Formula: see text]-adic lower bounds for linear forms in [Formula: see text]-adic logarithms of rational numbers using Padé approximations of the second kind.
Seppälä Louna, Palojärvi Neea
openaire +4 more sources
On sums of k-generalized Fibonacci and k-generalized Lucas numbers as first and second kinds of Thabit numbers [PDF]
Notes on Number Theory and Discrete MathematicsLet (Fᵣ⁽ᵏ⁾)ᵣ≥2-k and (Lᵣ⁽ᵏ⁾)ᵣ≥2-k be generalizations of the Fibonacci and Lucas sequences, where k≥2. For these sequences the initial k terms are 0,0,...,0, 1 and 0,0,...,2,1, and each subsequent term is the sum of the preceding k terms.
Hunar Sherzad Taher, Saroj Kumar Dash
doaj +1 more source
Linear forms in two logarithms and interpolation determinants [PDF]
Acta Arithmetica, 1994 The author provides a precise lower bound for the absolute value of a linear combination of two logarithms of real algebraic numbers with integer coefficients. This lower bound is explicit and improves in the real case an earlier result of \textit{M. Mignotte} and \textit{M. Waldschmidt} [Ann. Fac. Sci. Toulouse Math.
openaire +2 more sources