Now showing items 1-20 of 32

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      A proof of a trigonometric inequality. A glimpse inside the mathematical kitchen  [Article]

      Arias de Reyna Martínez, Juan; Van de Lune, Jan (2011-09)
      We prove the inequality ∞ ∑ k=1(−1) k+1 rk cos kφ k+2 < ∞ ∑ k=1 (−1) k+1 rk k+2 for 0 < r 1 and 0 < φ < π . For the case r = 1 we give two proofs. The first one is by means of a general numerical technique (Maximal Slope ...
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      A test for the Riemann hypotesis  [Article]

      Arias de Reyna Martínez, Juan (Adam Mickiewicz University, 2008-09)
      We prove that the Riemann Hypothesis holds if and only if I = Z +∞ 1 ˘ Π(x) − Li(x) ¯2 x −2 dx < +∞ with I = J, where J is some definite, computable real number (1.266 < J < 1.273). This provides us with a numerical test ...
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      Asymptotics of Keiper-Li coefficients  [Article]

      Arias de Reyna Martínez, Juan (Adam Mickiewicz University, Faculty of Mathematics and Computer Science, 2011)
      We show that the Riemann Hypothesis is equivalent to the assertion (ym)∈ℓ2 where ymym is defined by λm=1/2(logm+γ−log(2π)−1)+ym, and mλm represents the numbers in Xian-Jin Li's criterion. This confirms and further sharpens ...
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      Álgebras de Abel  [Article]

      Arias de Reyna Martínez, Juan (Real Academia de Ciencias Exactas, Físicas y Naturales, 1974)
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      Álgebras de Abel cerradas  [Article]

      Arias de Reyna Martínez, Juan (Real Academia de Ciencias Exactas, Físicas y Naturales, 1975)
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      Complejidad de los números naturales  [Article]

      Arias de Reyna Martínez, Juan (Real Sociedad Matemática Española, 2000)
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      Concentration of the distance in finite dimensional normed spaces  [Article]

      Arias de Reyna Martínez, Juan; Ball, Keith; Villa Caro, Rafael (University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics, 1998-12)
      We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ∥x − y∥ is more than √2(1 − ε). As a consecuence, we obtain a result proved by Bourgain, using QS-descomposition, ...
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      Counting tuples restricted by pairwise coprimality conditions  [Article]

      Arias de Reyna Martínez, Juan; Heyman, Randell (University of Waterloo, 2015)
      Given a subset A of the set {1, . . . , v}2 we say that (a1, . . . , av) exhibits pairwise coprimality over A if gcd(ai, aj ) = 1 for all (i, j) ∈ A. For a given positive x and a given set A we give an asymptotic formula ...
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      Definición y estudio de una función indefinidamente diferenciable de soporte compacto  [Article]

      Arias de Reyna Martínez, Juan (Real Academia de Ciencias Exactas, Físicas y Naturales, 1982)
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      Dynamical zeta functions and Kummer congruences  [Article]

      Arias de Reyna Martínez, Juan (Seminarjum Matematyczne Uniwersytetu, 2005)
      We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to settle positively the question of the existence of a map T : X → X such that the number of fixed ...
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      Los espacios (HM) y los cardinales medibles  [PhD Thesis]

      Facenda Aguirre, José Antonio (1981)
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      Espacios de sucesiones vectoriales  [PhD Thesis]

      Paúl Escolano, Pedro José (1985-07-10)
      Estudiamos en esta memoria dos problemas concretos sobre espacios de sucesiones vectoriales: Por un lado caracterizar las aplicaciones diagonales completamente continuas (i.e. que transforman acotados en relativamente ...
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      Factor de impacto de largo alcance  [Article]

      Arias de Reyna Martínez, Juan (Real Sociedad Matemática Española, 2014)
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      Funciones derivables en cuaterniones  [Article]

      Arias de Reyna Martínez, Juan (Real Sociedad Matemática Española, 1975)
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      I ∞ 0 (∑) no es totalmente tonelado  [Article]

      Arias de Reyna Martínez, Juan (Real Academia de Ciencias Exactas, Físicas y Naturales, 1985)
      Let ∑ be an infinite σ-field and denote by I ∞ 0 (∑) the space spanned by the characteristic functions of elements of ∑, endowed with the supremum norm. We prove that I ∞ 0 (∑) is not totally barrelled.
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      Integración en álgebras de Abel  [Article]

      Arias de Reyna Martínez, Juan (Real Academia de Ciencias Exactas, Físicas y Naturales, 1974)
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      Medidas cónicas y rangos de medidas vectoriales  [PhD Thesis]

      Romero Moreno, María del Carmen (1996)
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      Non Baire measure spaces  [Article]

      Arias de Reyna Martínez, Juan (Institut de Matemàtica, Universitat de Barcelona, 1983)
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      On some oscillating sums  [Article]

      Van de Lune, Jan; Arias de Reyna Martínez, Juan (2008)
      This paper deals with the sums S α (n)=∑ j=1 n (-1) ⌊jα⌋ where α is any real number. The interest in these sums was initiated by a problem proposed by H. D. Ruderman [Problem 6105, Am. Math. Mon. 83, 573 (1977)] and solved ...
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      On the distribution (mod 1) of the normalized zeros of the Riemann Zeta-function  [Article]

      Arias de Reyna Martínez, Juan (Elsevier, 2015-08)
      We consider the problem whether the ordinates of the non-trivial zeros of ζ(s) are uniformly distributed modulo the Gram points, or equivalently, if the normalized zeros (xn) are uniformly distributed modulo 1. Odlyzko ...