Displaying similar documents to “On the number of integer points in the displaced circles”

Gaps between consecutive divisors of factorials

Daniel Berend, J. E. Harmse (1993)

Annales de l'institut Fourier

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The set of all divisors of n ! , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest n ! and obtain a lower bound on their distance.

New variants of Khintchine's inequality.

Ioan Serb (2001)

Collectanea Mathematica

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Variants of Khintchine's inequality with coefficients depending on the vector dimension are proved. Equality is attained for different types of extremal vectors. The Schur convexity of certain attached functions and direct estimates in terms of the Haagerup type of functions are also used.