Estimates of Averaging Sums

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter III in Introduction to Diophantine Approximations, 1995, pp 35-49 from Springer

Abstract: Abstract Let again α be an irrational real number. In considering the values R(nα), it is natural to form the sum and to estimate its order of magnitude. Since one expects the values R(nα) to be somewhat evenly distributed around 1/2, it is then better to investigate immediately the sum which gives the average discrepancy between 1/2N and the sum of the remainders. We shall estimate this discrepancy in terms of a type for α.

Keywords: Fourier Series; Fourier Coefficient; Dirichlet Series; Absolute Constant; Proper Part (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-1-4612-4220-8_3

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