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On Bhargava's factorials of the set of twin primes in Z and in Fq[T]

Abstract : Assuming Dickson's conjecture, we give explicit formulas for Bhargava's factorials associated to the set P-2 of twin primes. We also characterize the polynomials of degree n which take integral values on P-2 by means of their values on {1,..., 2n+1}. Doing this, we give a negative answer to a conjecture of Mingarelli. Similar results are also obtained when replacing Z by F-q[T].
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https://hal.archives-ouvertes.fr/hal-01689000
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Submitted on : Saturday, January 20, 2018 - 12:51:58 AM
Last modification on : Friday, August 5, 2022 - 11:23:14 AM

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David Adam, Jean-Luc Chabert. On Bhargava's factorials of the set of twin primes in Z and in Fq[T]. International Journal of Number Theory, 2015, 11 (06), pp.1941-1959. ⟨10.1142/S1793042115500840⟩. ⟨hal-01689000⟩

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