Displaying similar documents to “Asymptotic distribution of poles and zeros of best rational approximants to x α on [0,1]”

An analogue of Montel’s theorem for some classes of rational functions

R. K. Kovacheva, Julian Lawrynowicz (2002)

Czechoslovak Mathematical Journal

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For sequences of rational functions, analytic in some domain, a theorem of Montel’s type is proved. As an application, sequences of rational functions of the best L p -approximation with an unbounded number of finite poles are considered.

An Alternative Form of the Functional Equation for Riemann’s Zeta Function, II

Andrea Ossicini (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper treats about one of the most remarkable achievements by Riemann, that is the symmetric form of the functional equation for ζ ( s ) . We present here, after showing the first proof of Riemann, a new, simple and direct proof of the symmetric form of the functional equation for both the Eulerian Zeta function and the alternating Zeta function, connected with odd numbers. A proof that Euler himself could have arranged with a little step at the end of his paper “Remarques sur un beau...

Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions

James Haglund (2011)

Open Mathematics

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Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show...