Tomás Oliveira e Silva

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This paper presents some results concerning the search for initial values to the so-called 3x+1 problem which give rise either to function iterates that attain a maximum value higher than all function iterates for all smaller initial values, or which have a stopping time higher than those of all smaller initial values. Our computational results suggest that(More)
– In this tutorial paper we present a generalization of the transversal filter, called Laguerre filter, and study some of its more remarkable properties. This filter is obtained by replacing each delay of the transversal filter by a first order all-pass section, and by applying a first order low-pass filter (with the same pole used in the all-pass sections)(More)
In this report we present a collection of results concerning two families of rational orthonormal functions, one on the unit circle, and another on the imaginary axis. We also describe in detail an interesting link between the two families. Special cases of these rational orthonormal functions include the Laguerre and Kautz orthonormal functions, as well as(More)
– This article presents a self-contained description of the method proposed by Deléglise and Rivat — which has roots on earlier work by Meissel, by Lehmer, and by Lagarias, Miller and Odlyzko — to compute π(x), which is the number of primes not larger than x. To make life easier to programmers, the major parts of the computation of π(x) are also presented(More)