On a problem of W. M. Schmidt concerning one-sided irregularities of point distributions (Q1106883)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On a problem of W. M. Schmidt concerning one-sided irregularities of point distributions |
scientific article; zbMATH DE number 4063209
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a problem of W. M. Schmidt concerning one-sided irregularities of point distributions |
scientific article; zbMATH DE number 4063209 |
Statements
On a problem of W. M. Schmidt concerning one-sided irregularities of point distributions (English)
0 references
1989
0 references
Answering a question of W. M. Schmidt, we prove that, given N points in the unit torus, there is a disc of diameter \(\leq 1\) containing definitely more given points than its expected value, and similarly, there is another disc of diameter \(\leq 1\) containing definitely less given points than its expected value. The order of magnitude of the discrepancy is greater than (log N)\({}^{-\epsilon}\) in both directions.
0 references
modified Rademacher functions
0 references
Riesz product
0 references
unit torus
0 references
discrepancy
0 references
0.8600980639457703
0 references
0.824007511138916
0 references
0.8237817287445068
0 references
