Schindler, D. and Sofos, E. (2019) Sarnak’s saturation problem for complete intersections. Mathematika, 65(1), pp. 1-56. (doi: 10.1112/s002557931800030x)
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Abstract
We study almost prime solutions of systems of Diophantine equations in the Birch setting. Previous work shows that there exist integer solutions of size B with each component having no prime divisors below B 1/u , where u equals c0n 3/2 , n is the number of variables and c0 is a constant depending on the degree and the number of equations. We improve the polynomial growth n 3/2 to the logarithmic (log n)(log log n) −1 . Our main new ingredients are the generalization of the Brudern–Fouvry vector sieve in any dimension and the incorporation of smooth ¨ weights into the Davenport–Birch version of the circle method.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Sofos, Dr Efthymios |
| Authors: | Schindler, D., and Sofos, E. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Mathematika |
| Publisher: | London Mathematical Society |
| ISSN: | 0025-5793 |
| ISSN (Online): | 2041-7942 |
| Published Online: | 24 August 2018 |
| Copyright Holders: | Copyright © 2018 University College London |
| First Published: | First published in Mathematika 65(1): 1-56 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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