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Artículo
A test for the Riemann hypotesis
(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 ...
Artículo
On some oscillating sums
(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 ...
Artículo
Complejidad de los números naturales
(Real Sociedad Matemática Española, 2000)
Artículo
Dynamical zeta functions and Kummer congruences
(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 ...