Lectures on Multiple Zeta Values IMSC 2011 by Michel Waldschmidt
نویسنده
چکیده
If true, this property would mean that there is no interesting algebraic structure. There are very few results on the arithmetic nature of these numbers, even less on their independence: it is known that π is a transcendental numbers, hence, so are all ζ(2n), n ≥ 1. It is also known that ζ(3) is irrational (Apéry, 1978), and that infinitely many ζ(2n+ 1) are irrational (further sharper results have been achieved by T. Rivoal and others – see [9, 14, 5]). But so far, it has not been disproved that all these numbers lie in the ring Q[π] (see the Open Problem 2).
منابع مشابه
Lectures on Multiple Zeta Values IMSC 2011
If true, this property would mean that there is no interesting algebraic structure. There are very few results on the arithmetic nature of these numbers, even less on their independence: it is known that π is a transcendental numbers, hence, so are all ζ(2n), n ≥ 1. It is also known that ζ(3) is irrational (Apéry, 1978), and that infinitely many ζ(2n+ 1) are irrational (further sharper results ...
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