On the uniform distribution modulo one of some subsequences of polynomial sequences
β Scribed by Jean Coquet
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 228 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper, we prove: "Suppose \(\alpha\) is an irrational number and let \(\|y\|\) denote the smallest distance of \(y\) from an integer. Then, for any real number \(\beta\), there are infinitely many primes \(p\) such that \(\|\alpha p-\beta\|<p^{-4 / 13}\)." 1993 Academic Press, Inc.
A famous inequality of ErdΓΆs and TurΓ‘n 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