12 results on '"Pablo Andres Panzone"'
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2. An irrationality result for a recursive construction
- Author
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Pablo Andres Panzone
- Subjects
Pure mathematics ,Mathematics::Dynamical Systems ,Series (mathematics) ,Simple (abstract algebra) ,Mathematics::Number Theory ,General Mathematics ,Irrational number ,Mathematics::History and Overview ,Irrationality ,Quotient ,Mathematics - Abstract
By simple means we prove irrationality results for some series whose terms are recursively defined. In particular, we prove that the roots and the quotient of such series are irrational numbers.
- Published
- 2021
3. On a paper of Dressler and Van de Lune
- Author
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Pablo Andres Panzone
- Subjects
Combinatorics ,Lune ,General Mathematics ,Arithmetic function ,Natural number ,Prime (order theory) ,Mathematics - Abstract
If $$z\in {\mathbb {C}}$$ and $$1\le n$$ is a natural number then $$\begin{aligned} \sum _{d_1 d_2 =n} (1-z^{p_1})\cdots (1-z^{p_m}) z^{q_1 e_{1}+\cdots +q_i e_{i} }=1, \end{aligned}$$ where $$d_1=p_1^{r_1}\dots p_m^{r_m }$$ , $$d_2=q_1^{e_1}\dots q_i^{e_i }$$ are the prime decompositions of $$d_1, d_2$$ . This is one of the identities involving arithmetic functions that we prove using ideas from the paper of Dressler and van de Lune [3].
- Published
- 2020
4. Integrales de ciertas series de Dirichlet
- Author
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Pablo Andres Panzone
- Subjects
symbols.namesake ,Pure mathematics ,Dirichlet Series ,General Mathematics ,symbols ,Integrales ,Integrals ,Dirichlet series ,Series de Dirichlet ,Mathematics - Abstract
We compute in closed form the integrals of certain expressions involving a class of Dirichlet series. This is a generalization of a formula of Jonathan Borwein to a problem stated (and solved) by A. Ivić. Resumen: Calculamos en forma cerrada integrales de ciertas expresiones que involucran una clase de series de Dirichlet. Esto es una generalización de una fórmula de Jonathan Borwein a un problema enunciado (y resuelto) por A. Ivić.
- Published
- 2020
5. Formulas for the Riemann zeta-function and certain Dirichlet series
- Author
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Pablo Andres Panzone
- Subjects
Pure mathematics ,Mathematics::Complex Variables ,Mathematics::General Mathematics ,Matemáticas ,Mathematics::Number Theory ,Applied Mathematics ,Mathematics::Classical Analysis and ODEs ,Mathematics::Spectral Theory ,Riemann zeta function ,Ramanujan's sum ,Matemática Pura ,symbols.namesake ,Riemann hypothesis ,Fourier transform ,symbols ,DIRICHLET SERIES ,RIEMANN ZETA-FUNCTION ,FOURIER TRANSFORM ,Analysis ,Dirichlet series ,CIENCIAS NATURALES Y EXACTAS ,Mathematics - Abstract
Using formulas of G. Hardy and S. Ramanujan we give several integral formulas for the Riemann zeta function and two Dirichlet series. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
- Published
- 2018
6. Combinatorial and modular solutions of some sequences with links to certain conformal map
- Author
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Pablo Andres Panzone
- Subjects
Physics ,MODULAR SOLUTIONS ,SEQUENCES ,Matemáticas ,Plane (geometry) ,General Mathematics ,Modular form ,Generating function ,purl.org/becyt/ford/1.1 [https] ,Conformal map ,Function (mathematics) ,Type (model theory) ,CONFORMAL MAPPING ,Matemática Pura ,Apéry's constant ,Combinatorics ,purl.org/becyt/ford/1 [https] ,CIENCIAS NATURALES Y EXACTAS ,Free parameter - Abstract
If fn is a free parameter, we give a combinatorial closed form solution of the recursion (n + 1)2un+1 − fnun − n 2un−1 = 0, n ≥ 1, and a related generating function. This is used to give a solution to the Apéry type sequence rnn3 + rn−1nαn3 −3α2n+α+ 2θon − θo+ rn−2(n − 1)3 = 0, n ≥ 2, for certain parameters α, θ. We show from another viewpoint two independent solutions of the last recursion related to certain modular forms associated with a problem of conformal mapping: Let f(τ) be a conformal map of a zero-angle hyperbolic quadrangle to an open half plane with values 0, ρ, 1, ∞ (0 < ρ < 1) at the cusps and define t = t(τ) := 1ρf(τ)f(τ)−ρ(τ)−1. Then the function E(τ) = 12πif0(τ)f(τ)11 −f(τ)ρ is a solution, as a generating function in the variable t, of the above recurrence. In other words, E(τ) = r0 +r1t+r2t 2 +. . . , where r0 = 1, r1 = −θ, α = 2− 4ρ. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
- Published
- 2018
7. SEPARATION PROPERTIES FOR ITERATED FUNCTION SYSTEMS OF BOUNDED DISTORTION
- Author
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Pablo Andres Panzone and Mariano Andrés Ferrari
- Subjects
Discrete mathematics ,Matemáticas ,Applied Mathematics ,purl.org/becyt/ford/1.1 [https] ,Minkowski–Bouligand dimension ,Dimension function ,OVERLAPPING ,Effective dimension ,Measure (mathematics) ,FRACTALS ,Matemática Pura ,purl.org/becyt/ford/1 [https] ,Modeling and Simulation ,Hausdorff dimension ,Outer measure ,Hausdorff measure ,Geometry and Topology ,HAUSDORFF DIMENSION ,CIENCIAS NATURALES Y EXACTAS ,Separation property ,Mathematics - Abstract
In this paper we study a general separation property for subsystems G, whose attractor KG is a sub-self-similar set. This is a generalization of the Lau-Ngai weak separation property for the bounded distortion case. For subsystems with positive Hausdorff measure in its similarity dimension, we characterize the subsets of KG with positive measure where the separation property may fail. We exhibit two examples of fractal sets, one not satisfying the weak separation property and whose existence was questioned by Zerner, the other having positive Hausdorff measure in its dimension and with the separation property failing on a subset of positive measure. Fil: Panzone, Pablo Andres. Universidad Nacional de la Patagonia; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina Fil: Ferrari, Mariano Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
- Published
- 2011
8. On the generating functions of Mersenne and Fermat primes
- Author
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Pablo Andres Panzone
- Subjects
Discrete mathematics ,Pure mathematics ,Mathematics::General Mathematics ,Mathematics::Number Theory ,Applied Mathematics ,General Mathematics ,Otras Ciencias Naturales y Exactas ,Mathematics::History and Overview ,Mersenne prime ,Fermat's theorem on sums of two squares ,Prime number ,purl.org/becyt/ford/1.7 [https] ,Safe prime ,Data_CODINGANDINFORMATIONTHEORY ,Wieferich prime ,Repunit ,purl.org/becyt/ford/1 [https] ,TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES ,MERSENNE PRIMES ,ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION ,Double Mersenne number ,FERMAT PRIMES ,CIENCIAS NATURALES Y EXACTAS ,Mathematics ,Fermat number - Abstract
With the aid of Solomon Golomb formula we give closed formulas for the generating functions of Mersenne and Fermat primes. A limit-type criteria for the existence of an infinite number of such primes is given using these generating functions. Fil: Panzone, Pablo Andres. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina
- Published
- 2010
9. Algebraic sequences for ζ(3) and a hybrid Catalan's constant†
- Author
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Pablo Andres Panzone and Luis Amadeo Piovan
- Subjects
Discrete mathematics ,MODULAR FORMS ,Matemáticas ,Applied Mathematics ,Modular form ,SPECIAL SEQUENCES ,Catalan's constant ,language.human_language ,Matemática Pura ,language ,Catalan ,Algebraic number ,Constant (mathematics) ,CIENCIAS NATURALES Y EXACTAS ,Analysis ,Mathematics - Abstract
We give two examples of algebraic sequences arising from modular forms which are good approximations for ζ(3) and the hybrid constant 8C+(π2/√2) where C=σ∞ 0 (-1)n/(2n+1)2 is Catalan's constant. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina Fil: Piovan, Luis Amadeo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
- Published
- 2009
10. On a Formula of S. Ramanujan
- Author
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Pablo Andres Panzone
- Subjects
Pure mathematics ,Matemáticas ,General Mathematics ,Ramanujan summation ,Ramanujan ,Rational function ,Ramanujan's congruences ,Ramanujan's sum ,Matemática Pura ,Ramanujan theta function ,symbols.namesake ,Simple (abstract algebra) ,Identity ,symbols ,Ramanujan tau function ,Ramanujan prime ,CIENCIAS NATURALES Y EXACTAS ,Mathematics - Abstract
Certain finite families of rational functions have the property that the coefficients of the expansions in power series of their elements are related by simple algebraic expressions. We prove an identity in the spirit of S. Ramanujan using a result of T. N. Sinha. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina
- Published
- 2015
11. Tiling the Plane with Different Hexagons and Triangles
- Author
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Pablo Andres Panzone
- Subjects
Physics ,Square tiling ,Matemáticas ,Plane (geometry) ,General Mathematics ,DIFFERENT HEXAGONS ,010102 general mathematics ,Trihexagonal tiling ,DIFFERENT TRIANGLES ,Geometry ,01 natural sciences ,Triangular tiling ,Matemática Pura ,Combinatorics ,0101 mathematics ,Arrangement of lines ,CIENCIAS NATURALES Y EXACTAS ,Rhombille tiling ,TILINGS ,Hexagonal tiling - Abstract
We prove that the plane can be tiled with equilateral triangles and regular hexagons of integer sides using exactly one of each family. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
- Published
- 2016
12. A generalization of Iseki's formula
- Author
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Luis Amadeo Piovan, Pablo Andres Panzone, and Mariano Andrés Ferrari
- Subjects
purl.org/becyt/ford/1 [https] ,ISEKI'S TRANSFORMATION FORMULA ,Generalization ,Matemáticas ,General Mathematics ,purl.org/becyt/ford/1.1 [https] ,TRANSFORMATION FORMULAE ,Transformation formulae ,Iseki's transformation formula ,Humanities ,CIENCIAS NATURALES Y EXACTAS ,Mathematics ,Matemática Pura - Abstract
We prove a generalization of Iseki's transformation formula, which is basically a transformation formula for infinite products with certain variable exponents. We note that an infinite number of transformation formulae may be derived from this generalization and, as a corollary, a particular case is given. Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina Fil: Piovan, Luis Amadeo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Bahía Blanca. Instituto de Matemática Bahía Blanca (i); Argentina. Universidad Nacional del Sur. Departamento de Matemática; Argentina Fil: Ferrari, Mariano Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentina
- Published
- 2011
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