Comptes Rendus
Number Theory
Estimation of certain exponential sums arising in complexity theory
Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 627-631.

It is shown that the correlation on {0,1}n between parity and a polynomial p(x1,,xn)Z[X1,,Xn](modq), q a fixed odd number and p(X) of degree d arbitrary but fixed, is exponentially small in n as n. An application to circuit complexity, from where the problem originates, is given.

On démontre que la corrélation sur {0,1}n de la fonction parité et un polynôme p(x1,,xn)Z[X1,,Xn](modq), q un entier impair donné et p(X) de degré d arbitraire mais fixé, est exponentiellement petite en n pour n. On obient une application en théorie de complexité où la question trouve son origine.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.03.008
Jean Bourgain 1

1 Institute for Advanced Study, Princeton, NJ 08540, USA
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Jean Bourgain. Estimation of certain exponential sums arising in complexity theory. Comptes Rendus. Mathématique, Volume 340 (2005) no. 9, pp. 627-631. doi : 10.1016/j.crma.2005.03.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.03.008/

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[5] A. Hajnal; W. Maass; P. Pudlák; M. Szegedy; G. Turán Threshold circuits of bounded depth, J. Comput. System Sci., Volume 46 (1993) no. 2, pp. 129-154

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