Linear equations in variables which lie in a multiplicative group
| dc.creator | Evertse, J. -H. | |
| dc.creator | Schlickewei, H. P. | |
| dc.creator | Schmidt, W. M. | |
| dc.date | 2004-09-30 | |
| dc.date.accessioned | 2026-07-07T05:12:45Z | |
| dc.date.available | 2026-07-07T05:12:45Z | |
| dc.description | Let K be a field of characteristic 0 and let n be a natural number. Let Gamma be a subgroup of the multiplicative group $(K^\ast)^n$ of finite rank r. Given $A_2,...,a_n\in K^\ast$ write $A(a_1,...,a_n,Γ)$ for the number of solutions x=(x_1,...,x_n)\in Γ$ of the equation a_1x_1+...+a_nx_n=1$, such that no proper subsum of $a_1x_1+...+a_nx_n$ vanishes. We derive an explicit upper bound for $A(a_1,...,a_n,Γ)$ which depends only on the dimension n and on the rank r. | |
| dc.identifier | https://arxiv.org/abs/math/0409604 | |
| dc.identifier | http://arxiv.org/abs/math/0409604 | |
| dc.identifier | Ann. of Math. (2), Vol. 155 (2002), no. 3, 807--836 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72695 | |
| dc.subject | Number Theory | |
| dc.title | Linear equations in variables which lie in a multiplicative group | |
| dc.type | text |