On the Local Solubility of Diophantine Systems |
| |
Authors: | Trevor D Wooley |
| |
Institution: | (1) Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109–1003, U.S.A. |
| |
Abstract: | Let p be a rational prime number. We refine Brauer's elementary diagonalisation argument to show that any system of r homogeneous polynomials of degree d, with rational coefficients, possesses a non-trivial p-adic solution provided only that the number of variables in this system exceeds (rd
2)2d-1. This conclusion improves on earlier results of Leep and Schmidt, and of Schmidt. The methods extend to provide analogous conclusions in field extensions of Q, and in purely imaginary extensions of Q. We also discuss lower bounds for the number of variables required to guarantee local solubility. |
| |
Keywords: | local solubility diophantine equations forms in many variables p-adic fields |
本文献已被 SpringerLink 等数据库收录! |
|