Irrationality of and

✍ Scribed by Kelly Postelmans; Walter Van Assche

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 288 KB
• Volume: 126
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.11.011

✦ Synopsis

In this paper we show how one can obtain simultaneous rational approximants for ζ q (1) and ζ q (2) with a common denominator by means of Hermite-Padé approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, ζ q (1), ζ q (2) are linearly independent over Q. In particular this implies that ζ q (1) and ζ q (2) are irrational. Furthermore we give an upper bound for the measure of irrationality.