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The series is convergent when s is a complex number with <(s) > 1. Some special values of ζ(s) are well known, for example the values ζ(2) = π/6, ζ(4) = π/90, were obtained by Euler. In 1859, Riemann… (More)
This survey presents a unified and essentially self-contained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and… (More)
Ž . ABSTRACT: In a randomly grown binary search tree BST of size n, any fixed pattern occurs with a frequency that is on average proportional to n. Deviations from the average case are highly… (More)
We present a unified analytic framework dedicated to the estimation of the size of the largest component in random combinatorial structures.
A unifiedtreatmentof parametersrelevant to factoringpolynomialsover finite fieldsis given. Theframework isbasedongeneratingfunctionsfor describingparametersof interest andon singularityanalysisfor… (More)
We give algorithms to compute the asymptotic expansion of solutions of linear recurrences with rational coefficients and rational initial conditions in polynomial time in the order of the recurrence.
We expose techniques that permit to approximate the Riemann Zeta function in different context. The motivation does not restrict only to the numerical verification of the Riemann hypothesis (see… (More)
In a randomly grown binary search tree (BST) of size n, any xed pattern occurs with a frequency that is on average proportional to n. Deviations from the average case are highly unlikely and well… (More)
A b s t r a c t . We consider the largest degrees that occur in the decomposition of polynomials over finite fields into irreducible factors. We expand the range of applicability of the Dickman… (More)
In this article, we report on computations that led to the discovery of a new Lehmer pair of zeros for the Riemann ζ function. Given this new close pair of zeros, we improve the known lower bound for… (More)