Arithmetics of Linear Forms Involving Odd Zeta Values
نویسندگان
چکیده
The story exposed in this paper starts in 1978, when R. Apéry [Ap] gave a surprising sequence of exercises demonstrating the irrationality of ζ(2) and ζ(3). (For a nice explanation of Apéry’s discovery we refer to the review [Po].) Although the irrationality of the even zeta values ζ(2), ζ(4), . . . for that moment was a classical result (due to L. Euler and F. Lindemann), Apéry’s proof allows one to obtain a quantitative version of his result, that is, to evaluate irrationality exponents:
منابع مشابه
Arithmetic of Linear Forms Involving Odd Zeta Values
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of ζ(2) and ζ(3), as well as to explain Rivoal’s recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers ζ(5), ζ(7), ζ(9), and ζ(11) i...
متن کامل2 1 Ju n 20 02 Arithmetic of linear forms involving odd zeta values ∗
A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of ζ(2) and ζ(3), as well as to explain Rivoal’s recent result (math.NT/0008051) on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers ζ(5), ζ(7),...
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تاریخ انتشار 2001