The zeta-regularized product of odious numbers
Résumé
What is the product of all odious integers, i.e., of all integers whose binary expansion contains an odd number of 1's? Or more precisely, how to define a product of these integers which is not infinite, but still has a “reasonable” definition? We will answer this question by proving that this product is equal to , where γ and φ are respectively the Euler-Mascheroni and the Flajolet-Martin constants.
Domaines
Mathématiques [math]
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Allouche - 2021 - The zeta-regularized product of odious numbers.pdf (118.39 Ko)
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