Baker's conjecture for functions with real zeros
نویسندگان
چکیده
منابع مشابه
Real entire functions with real zeros and a conjecture of Wiman
This conclusion is not true for the first derivative as the example exp(sin z) shows. For real entire functions with finitely many zeros, all of them real, Theorem 1.1 was proved in [3]. Theorem 1.1 can be considered as an extension to functions of infinite order of the following result of Sheil-Small [20], conjectured by Wiman in 1914 [1, 2]. For every integer p ≥ 0, denote by V2p the set of e...
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is said to be typically-real of order p, if in (1.1) the coefficients bn are all real and if either (I) f(z) is regular in |a| =S1 and 3/(ei9) changes sign 2p times as z = eie traverses the boundary of the unit circle, or (II) f(z) is regular in | z\ < 1 and if there is a p < 1 such that for each r in p<r<l, $f(reie) changes sign 2p times as z = reie traverses the circle \z\ =r. This set of fun...
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A small part of the Generalized Riemann Hypothesis asserts that L-functions do not have zeros on the line segment ( 2 , 1]. The question of vanishing at s = 2 often has deep arithmetical significance, and has been investigated extensively. A persuasive view is that L-functions vanish at 2 either for trivial reasons (the sign of the functional equation being negative), or for deep arithmetical r...
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Let φ and f be functions in the Laguerre–Pólya class. Write φ(z) = e−αzφ1(z) and f (z) = e−βzf1(z), where φ1 and f1 have genus 0 or 1 and α,β 0. If αβ < 1/4 and φ has infinitely many zeros, then φ(D)f (z) has only simple real zeros, where D denotes differentiation. 2004 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2018
ISSN: 0024-6115
DOI: 10.1112/plms.12124