Averages of short exponential sums. II (Q2773296)
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: Averages of short exponential sums. II |
scientific article; zbMATH DE number 1709889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Averages of short exponential sums. II |
scientific article; zbMATH DE number 1709889 |
Statements
21 February 2002
0 references
averages of short exponential sums
0 references
rational functions of several variables
0 references
Averages of short exponential sums. II (English)
0 references
Recently [Acta Arith. 88, 223-231 (1999; Zbl 0936.11048)], the author presented a technique to estimate certain averages of short exponential sums of type NEWLINE\[NEWLINE \sum_{P \leq p \leq 2P} \sum_{1 \leq m \leq M} \left|\sum_{1 \leq n \leq N} e \left(\frac{m r(n)}{p} \right) \right|^2~~. NEWLINE\]NEWLINE In the present paper he generalizes earlier results to rational functions of several variables. One new feature is the appearance of an obstruction caused by a certain Diophantine equation, the size of the set of solutions which controls the size of the exponential sums.
0 references
