Functions of One Complex Variable

Conway, John B.

doi:10.1007/978-1-4615-9972-2

Cited by 688 publications

(559 citation statements)

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“…As functions on the complex plane, such transformations are called Möbius transformations, and play an important role in the study of analytic mappings on the complex plane; see eg. [3,Chapter 3] or [1,Chapter 3]. Any invertible rational function is certainly 1-to-1 on its domain, but the converse (oddly) is not true.…”

Section: Setting the Stage For The Investigationmentioning

confidence: 99%

$$N$$ N -Tupling Transformations and Invariant Definite Integrals

Cochrane

Goldstein

2015

Int. J. Appl. Comput. Math

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Section: Setting the Stage For The Investigationmentioning

confidence: 99%

$$N$$ N -Tupling Transformations and Invariant Definite Integrals

Cochrane

Goldstein

2015

Int. J. Appl. Comput. Math

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“…By the Weierstrass Factorisation Theorem ( [6], VII.5.14) and (28), there exist entire functions g 1 (s), g 2 (s) such that…”

Section: Lemma 26mentioning

confidence: 99%

“…Since we have assumed that 1 2 + it is not a zero or pole of Z P (s), the function f P (w) is holomorphic in a neighbourhood of the closed disc S, centred at a, of radius a − 1 2 . As this disc contains the interval from 1 2 to a, we may apply Jensen's Formula ( [6], XI.1.2) to conclude that…”

Section: Lemma 34 N (T) = O(t D )mentioning

confidence: 99%

A prime geodesic theorem for SL4

Deitmar

Pavey

2007

Ann Glob Anal Geom

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“…The idea to show this is to compare C n to a function whose zeros are precisely equally distributed, namely h(z) = z n+1 − 1, and use Rouché's Theorem (see [5], p. 125). Now, we can state our second result .…”

Section: Statement Of Theoremsmentioning

confidence: 99%

Zeros of cesàro sum approximations

Barnard

Pearce

Wheeler

2001

Complex Variables, Theory and Application: An International Jou

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Abstract.Let D denote the open unit disk and let f (z) = ∞ n=0 anz n be analytic on D with positive monotone decreasing coefficients an. We answer several questions posed by J. Cima on the location of the zeros of polynomial approximants which he originally posed about outer functions. In particular, we show that the zeros of Cesàro approximants to f are well-behaved in the following sense: (1) if an a n+1 → 1, and a 0 am ≤ am b , then ∂D is the only accumulation set for the zeros of the Cesàro sums of f ; and (2) if f has a representation f (z) = ∞ n=0 g 1 n+c z n where g(x) = ∞ n=0 bnx n ≡ 0, bn ≥ 0, then we give sufficient conditions so that the convex hull of the zeros of the Cesàro sums of f will contain D.

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Functions of One Complex Variable

Cited by 688 publications

References 0 publications

$$N$$ N -Tupling Transformations and Invariant Definite Integrals

$$N$$ N -Tupling Transformations and Invariant Definite Integrals

A prime geodesic theorem for SL4

Zeros of cesàro sum approximations

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