Some remarks on Turán's inequality
✍ Scribed by S.P Zhou
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 155 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We prove a general Tura n Kubilius inequality and use it to derive that the number {(S) of divisors of an integer r\_r matrix S verifies {(S)=(Log |S|) Log 2+o(1) for all but o(X) matrices of determinant X. This is in sharp contrast with the average order which is Ä |S| ; r &1 (Log |S|) # r for ; r
A famous inequality of Erdös and Turán estimates the discrepancy \(\Delta\) of a finite sequence of real numbers by the quantity \(B=\min _{K} K^{-1}+\sum_{k=1}^{K-1}\left|\alpha_{k}\right| / k\), where the \(\alpha_{k}\) are the Fourier coefficients. We investigate how bad this estimate can be. We