A minimal area problem for nonvanishing functions
نویسندگان
چکیده
منابع مشابه
A Minimal Area Problem for Nonvanishing Functions
The minimal area covered by the image of the unit disk is found for nonvanishing univalent functions normalized by the conditions f(0) = 1, f ′(0) = α. Two different approaches are discussed, each of which contributes to the complete solution of the problem. The first approach reduces the problem, via symmetrization, to the class of typically real functions, where the well-known integral repres...
متن کاملNonvanishing Univalent Functions*
The class S of functions g(z) = z + c 2 z 2 + c 3 z 3 + ... analytic and univalent in the unit disk Izr < 1 has been thoroughly studied, and its properties are well known. Our purpose is to investigate another class of functions which, by contrast, seems to have been rather neglected. This is the class S o of functions f ( z ) = 1 + a 1 z + a 2 z Z + . . , analytic, univalent, and nonvanishing ...
متن کاملBounded Nonvanishing Functions and Bateman Functions
We consider the family B̃ of bounded nonvanishing analytic functions f(z) = a0 + a1 z + a2 z 2 + · · · in the unit disk. The coefficient problem had been extensively investigated (see e. g. [2], [13], [14], [16], [17], [18], [20]), and it is known that |an| ≤ 2 e for n = 1, 2, 3, and 4. That this inequality may hold for n ∈ IN, is known as the Krzyż conjecture. It turns out that for f ∈ B̃ with a...
متن کاملNonvanishing of certain Rankin-Selberg L-functions
In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...
متن کاملEffective Nonvanishing of Canonical Hecke L-functions
Motivated by work of Gross, Rohrlich, and more recently Kim, Masri, and Yang, we investigate the nonvanishing of central values of L-functions of “canonical” weight 2k−1 Hecke characters for Q( √ −p), where 3 < p ≡ 3 (mod 4) is prime. Using the work of Rodriguez-Villegas and Zagier, we show that there are nonvanishing central values provided that p ≥ 6.5(k−1) and (−1) ( 2 p ) = 1. Moreover, we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2006
ISSN: 1061-0022,1547-7371
DOI: 10.1090/s1061-0022-06-00941-1