François Hennecart

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In this paper we provide in Fp expanding lower bounds for two variables functions f (x, y) in connectionwith the product set or the sumset. The sum–product problem has been immensely studied in the recent past. A typical result in F∗p is the existence of ∆(α) > 0 such that if |A| ≍ p then max(|A + A|, |A · A|) ≫ |A|1+∆(α), Our aim is to obtain analogous(More)
About half a century ago, some authors, among others M. Kneser and G. A. Freiman, began a systematic study of what is now called “inverse additive number theory” (see [7] for a review of this theory and [12] for an extensive presentation). Roughly speaking, the general problematic is the following: extracting information on the structure of sets whose(More)
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(More)
The left-truncated generalized Poisson distribution belongs to the family of the modified power series distributions. Using sufficiency and completeness of £ ^ x . (minx , , $ 3 x 0 ) respectively, when the truncation point is known (resp. unknown), the minimum variance unbiased (M.V.U) estimator for certain functions of the parameter $ (resp. 0, r)(More)
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