2 citations · 6 across the 10 of their papers we have counts for
12 papers
Block-count constrained harmonic sums: spectral expansion and block-directed Euler-Maclaurin
Jean-François Burnol
We determine exactly how harmonic sums, taken over integers with a given number of occurrences of a fixed block of digits, depend on that number of occurrences. Language factorizat…
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…