Rational approximation to real points on quadratic hypersurfaces

Abstract: To each point of R^n we attach an exponent of approximation which quantifies "how well" we can approximate this point by rational points with same denominator. A fundamental question in Diophantine approximation is to determine the supremum of this exponent on given subsets of R^n. In a joint work with Roy, we recently answered this question for quadratic hypersurfaces Z of R^n defined over Q: the optimal exponent depends only on the Witt index (over Q) of the quadratic form defining Z. In dimension n = 2, we recover results of Roy while in higher dimension this completes recent work of Kleinbock and Moshchevitin.

number theory

Audience: researchers in the topic

Japan Europe Number Theory Exchange Seminar

Series comments: The purpose of the Japan Europe Number Theory Exchange Seminar is to give a opportunity for researchers in Japan and Europe to exchange their research projects by giving short talks (30 min). The target audience are researchers of any level in the area of number theory.

Start for Fall 2021: 26th October