The Beurling-Nyman criterion for the Riemann hypothesis: numerical aspects. (Le critère de Beurling et Nyman pour l'hypothèse de Riemann: aspects numérique.)
Étude probabiliste des sommes des puissances s-ièmes
Waring's problem for sixteen biquadrates. Numerical results
We explain the algorithms that we have implemented to show that all integers congruent to modulo in the interval are sums of five fourth powers, and that all integers congruent to or modulo in the interval are sums of seven fourth powers. We also give some results related to small sums of biquadrates. Combining with the Dickson ascent method, we deduce that all integers in the interval are sums of biquadrates.
Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi
Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of...
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