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4 results on '"Pablo Andres Panzone"'

1. Formulas for the Riemann zeta-function and certain Dirichlet series

Author

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

2. SEPARATION PROPERTIES FOR ITERATED FUNCTION SYSTEMS OF BOUNDED DISTORTION

Author

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

3. On the generating functions of Mersenne and Fermat primes

Author

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

4. Algebraic sequences for ζ(3) and a hybrid Catalan's constant†

Author

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

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