A famous inequality of Erdo(combining double acute accent)s and Turán estimates the discrepancy Δ of a finite sequence of real numbers by the quantity B = minKK-1 + ∑K - 1k = 1 |αk|/k, where the αk are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case Δ is of order B3/2.
ASJC Scopus subject areas
- Algebra and Number Theory