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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Differential identities


Authors: Bernard Beauzamy and Jérôme Dégot
Journal: Trans. Amer. Math. Soc. 347 (1995), 2607-2619
MSC: Primary 05A19; Secondary 11C08, 30C10
MathSciNet review: 1277095
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Abstract: We deal here with homogeneous polynomials in many variables and their hypercube representation, introduced in [5]. Associated with this representation there is a norm (Bombieri's norm) and a scalar product. We investigate differential identities connected with this scalar product. As a corollary, we obtain Bombieri's inequality (originally proved in [4]), with significant improvements.

The hypercube representation of a polynomial was elaborated in order to meet the requests of massively parallel computation on the "Connection Machine" at Etablissement Technique Central de l'Armement; we see here once again (after [3] and [5]) the theoretical power of the model.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1277095-1
PII: S 0002-9947(1995)1277095-1
Keywords: Polynomials, differential identities
Article copyright: © Copyright 1995 American Mathematical Society