On integral boxes of minimal surface
Generalising the two-dimensional case, we provide estimates for the mean-values of the lengths of the edges of an integral box with given volume and minimal surface.
math.NT↗
arXiv subjects
Jonathan Rotgé
Publications and source records attributed to Jonathan Rotgé.
\'Etude statistique du facteur premier m\'edian, 4: somme des inverses
We consider the sum of the reciprocals of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an asymptotic expansion in the first case and an asymptotic formula involving an implicit parameter in the second. Both these results improve on previous estimates available in the literature.
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Étude statistique du facteur premier médian, 2 : lois locales
We estimate the local laws of the distribution of the middle prime factor of an integer, defined according to multiplicity or not. An asymptotic estimate with effective remainder is provided for a wide range of values. In particular this enables to precisely describe the phase transition occurring in the relevant distribution.
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Étude statistique du facteur premier médian, 3 : lois de répartition
We consider the Gaussian limit law for the distribution of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an optimal bound for the speed of convergence, thereby improving on previous estimates available in the literature.
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\'Etude statistique du facteur premier m\'edian, 1 : valeur moyenne
We provide an asymptotic expansion for the mean-value of the logarithm of the middle prime factor of an integer, defined according to multiplicity or not, thus generalising a recent study of McNew, Pollack, and Singha Roy. This yields an improvement of the asymptotic estimate, in particular by furnishing an optimal remainder when the expansion is truncated at the first order.
math.NT↗