Trigonometric approximation and uniform distribution modulo one

Cochrane, Todd

doi:10.1090/S0002-9939-1988-0947641-5

Trigonometric approximation and uniform distribution modulo one
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Proc. Amer. Math. Soc. 103 (1988), 695-702 Request permission

Abstract:

We construct $n$-dimensional versions of the Beurling and Selberg majorizing and minorizing functions and use them to prove results on trigonometric approximation and to prove an $n$-dimensional version of the Erdös-Turán inequality. Finally, an application is given to counting solutions of polynomial congruences.

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