2 citations · 6 across the 10 of their papers we have counts for
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The asymptotic oscillations of moments related to Dirichlet series with missing digits
Jean-François Burnol
We prove that the (suitably rescaled) moments of certain discrete measures on the unit interval, which are related to the numerical evaluation of zeta series with missing digits in…
Some geometric series for Euler's constant
Jean-François Burnol
We provide representations of Euler's constant as series which converge geometrically fast (but use a certain sequence whose computation induces a quadratic cost). The…
On the analytic continuation of Dirichlet series with missing digits
Jean-François Burnol
We study the Dirichlet series associated with the integers whose radix- representation misses certain (fixed) digits. The existence of a meromorphic continuation to the entire c…
Some series representing the zeta function for
Jean-François Burnol
We represent the Riemann zeta function in the half-plane via series whose terms admit geometrically decreasing bounds. This is based upon simple combinatorics of certain…
Measures associated with certain ellipsephic harmonic series and the Allouche-Hu-Morin limit theorem
Jean-François Burnol
We consider the harmonic series over the integers having occurrences of a given block of -ary digits, of length , and relate them to certain meas…
Digamma function and general Fischer series in the theory of Kempner sums
Jean-François Burnol
The harmonic sum of the integers which are missing given digits in a base is expressed as plus corrections indexed by the excluded digits and expressed as inte…
On the asymptotics of Kempner-Irwin sums
Jean-François Burnol
Let be the subseries of the harmonic series keeping the integers having exactly occurrences of the digit in base . We prove the existence of an asymptotic exp…
Summing the "exactly one 42" and similar subsums of the harmonic series
Jean-François Burnol
For and a string of two digits in base , let be the subsum of the harmonic series with only those integers having exactly one occurrence of . We obtain a th…
Measures for the summation of Irwin series
Jean-François Burnol
We consider the series of reciprocals of those positive integers with exactly occurrences of a given -ary digit (Irwin series), and obtain geometrically convergent repre…
Moments in the exact summation of the curious series of Kempner type
Jean-François Burnol
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometric…
Entrelacement de co-Poisson
Jean-Francois Burnol
Une danse avec co-Poisson: 1 Introduction: Sommes, Propriete de support, Co-sommes, Mellin et dzêta, Fonctions entieres et meromorphes 2 Docteur Poisson et Mister Co: Des theoremes…