A Gel'fond type criterion in degree two

Details A Gel'fond type criterion in degree two A Gel'fond type criterion in degree two

2002-12-16

arxiv.org/abs/math/0212209v1

Acta Arithmetica 111.1 (2004), 97-103

Mathematics

Number Theory

6 pages

Scientific paper

We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two and height at most X, whose absolute value at that complex number is at most (1/4)X^{-(3+sqrt{5})/2}. We show that the exponent (3+sqrt{5})/2 in this condition is optimal, and deduce from this criterion a result of simultaneous approximation of a real number by conjugate algebraic numbers.

Affiliated with

Also associated with

No associations

Rating

A Gel'fond type criterion in degree two does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Gel'fond type criterion in degree two, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Gel'fond type criterion in degree two will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-426834