منابع مشابه
On the Mean Values of the Riemann Zeta-function in Short Intervals
It is proved that, for T ε ≤ G = G(T) ≤
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Using the Padé approximation of the exponential function, we obtain a general recurrence relation for values of the zeta function which contains, as particular cases, many of relations already proved. Applications to Bernoulli polynomials are given. At last, we derive some new recurrence relations with gap of length 4 for zeta numbers. MSC: 11B68 41A21
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1. Introduction. The irrationality of values of the zeta-function ζ(s) at odd integers s ≥ 3 is one of the most attractive problems in number theory. Inspite of a deceptive simplicity and more than two-hundred-year history of the problem, all done in this direction can easily be counted. It was only 1978, when Apéry [A] obtained the irrationality of ζ(3) by a presentation of " nice " rational a...
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We shall see that in these cases the spectra come from irreducible representations of G occurring in L2(Γ\G), and that the resulting integral transform of g has a kernel composed of Bessel functions of representations of G. It should be noted that (2) can readily be extended to any imaginary quadratic number field of class number one. Other examples that share the same structure and have been m...
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In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1989
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-52-4-367-371