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  • 1 U.F.R. de Mathématique (IRMA) Université Louis-Pasteur et C.N.R.S. 7 rue René Descartes, F-67084 Strasbourg Cedex, France 7 rue René Descartes, F-67084 Strasbourg Cedex, France
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Summary  

By applying the majorizing measure method, we obtain a new estimate  of the supremum of random  trigonometric sums. We show that this estimate is strictly stronger than the well-known Salem-Zygmund's estimate, as well as recent general formulations of it obtained by the author. This improvement is obtained by considering the case when the characters are indexed on  sub-exponentially growing sequences of integers. Several remarkable examples are studied.

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