InforLorV4, Main, Exploration, bibRecord, 001360

Numerical Approximation of the Masser-Gramain Constant to Four Decimal Digits: delta=1.819...

Identifieur interne : 001360 ( Main/Exploration ); précédent : 001359; suivant : 001361

Numerical Approximation of the Masser-Gramain Constant to Four Decimal Digits: delta=1.819...

Auteurs : Guillaume Melquiond [France] ; W. Georg Nowak [Autriche] ; Paul Zimmermann [France]

Source :

Mathematics of Computation [ 0025-5718 ] ; 2013.

RBID : Hal:hal-00644166

Abstract

We prove that the constant studied by Masser, Gramain, and Weber, satisfies 1.819776 < delta < 1.819833, and disprove a conjecture of Gramain. This constant is a two-dimensional analogue of the Euler-Mascheroni constant; it is obtained by computing the radius r_k of the smallest disk of the plane containing k Gaussian integers. While we have used the original algorithm for smaller values of k, the bounds above come from methods we developed to obtain guaranteed enclosures for larger values of k.

Url:

https://hal.inria.fr/hal-00644166

DOI: 10.1090/S0025-5718-2012-02635-4

Affiliations:

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<front><div type="abstract" xml:lang="en">We prove that the constant studied by Masser, Gramain, and Weber, satisfies 1.819776 < delta < 1.819833, and disprove a conjecture of Gramain. This constant is a two-dimensional analogue of the Euler-Mascheroni constant; it is obtained by computing the radius r_k of the smallest disk of the plane containing k Gaussian integers. While we have used the original algorithm for smaller values of k, the bounds above come from methods we developed to obtain guaranteed enclosures for larger values of k.</div>
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Numerical Approximation of the Masser-Gramain Constant to Four Decimal Digits: delta=1.819...

Numerical Approximation of the Masser-Gramain Constant to Four Decimal Digits: delta=1.819...

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