TY - JOUR
AB - We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over ℝ and over ℚp for all primes p, provided that the form has at least (d - 1/2 √d)2d variables. This improves on a longstanding result of Birch.
AU - Browning, Timothy D
AU - Prendiville, Sean
ID - 256
IS - 731
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
TI - Improvements in Birch's theorem on forms in many variables
VL - 2017
ER -