Recurrence Relations and the Algebraic Irrationality of Ζ(3)
نویسنده
چکیده
We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, we show that there exists a four-term real linear recurrence relation whose solutions allow us to produce a tractable equivalent criterion for the quadratic irrationality of ζ(3), where ζ is the classic Zeta function of Riemann or, for that matter, the quadratic irrationality of any other irrational that arises either as a result of an Apéry-like argument, or from a continued fraction expansion. The result is amplified to produce a criterion for the transcendence of such irrational numbers.
منابع مشابه
Principal Solutions of Recurrence Relations and Irrationality Questions in Number Theory
We apply the theory of disconjugate linear recurrence relations to the study of irrational quantities in number theory. In particular, for an irrational number associated with solutions of three-term linear recurrence relations we show that there exists a four-term linear recurrence relation whose solutions allow us to show that the number is a quadratic irrational if and only if the four-term ...
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