Irrationality exponents of generalized Hone series
نویسندگان
چکیده
منابع مشابه
Irrationality of certain infinite series
In this paper a new direct proof for the irrationality of Euler's number e = ∞ k=0 1 k! is presented. Furthermore, formulas for the base b digits are given which, however, are not computably effective. Finally we generalize our method and give a simple criterium for some fast converging series representing irrational numbers.
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The Euler characteristic of all the Chow varieties, of a fixed projective variety, can be collected in a formal power series called the Euler-Chow series. This series coincides with the Hilbert series when the Picard group is a finite generated free abelian group. It is an interesting open problem to find for which varieties this series is rational. A few cases have been computed, and it is sus...
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is irrational for every t >2 . By more complicated arguments one can show that the condition (ni, ni)=1 is superfluous. We do not give the details since I do not think that the condition E 1 /n i < oo is very relevant . In fact it could be replaced i=1 by a weaker but more complicated condition . I would expect that the series (2) is always irrational if n 7, jl-nk -~'co (perhaps even n k./ k->...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2020
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-020-01423-6