Brannan’s conjecture and trigonometric sums

Roger W. Barnard; Udaya C. Jayatilake; Alexander Yu Solynin

doi:10.1090/S0002-9939-2015-12398-2

Brannan’s conjecture and trigonometric sums

Roger W. Barnard, Udaya C. Jayatilake, Alexander Yu Solynin

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We prove some versions of Brannan’s Conjecture on Taylor coefficients of the ratio of two binomials of the form (1+zx)^α/(1−x)^β and discuss some related inequalities for trigonometric sums.

Original language	English
Pages (from-to)	2117-2128
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	5
DOIs	https://doi.org/10.1090/S0002-9939-2015-12398-2
State	Published - 2015

Keywords

Brannan’s conjecture
Trigonometric sums

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10.1090/S0002-9939-2015-12398-2

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title = "Brannan{\textquoteright}s conjecture and trigonometric sums",

abstract = "We prove some versions of Brannan{\textquoteright}s Conjecture on Taylor coefficients of the ratio of two binomials of the form (1+zx)α/(1−x)β and discuss some related inequalities for trigonometric sums.",

keywords = "Brannan{\textquoteright}s conjecture, Trigonometric sums",

author = "Barnard, {Roger W.} and Jayatilake, {Udaya C.} and Solynin, {Alexander Yu}",

note = "Publisher Copyright: {\textcopyright} 2014 American Mathematical Society.",

year = "2015",

doi = "10.1090/S0002-9939-2015-12398-2",

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volume = "143",

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AU - Barnard, Roger W.

AU - Jayatilake, Udaya C.

AU - Solynin, Alexander Yu

PY - 2015

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N2 - We prove some versions of Brannan’s Conjecture on Taylor coefficients of the ratio of two binomials of the form (1+zx)α/(1−x)β and discuss some related inequalities for trigonometric sums.

AB - We prove some versions of Brannan’s Conjecture on Taylor coefficients of the ratio of two binomials of the form (1+zx)α/(1−x)β and discuss some related inequalities for trigonometric sums.

KW - Brannan’s conjecture

KW - Trigonometric sums

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U2 - 10.1090/S0002-9939-2015-12398-2

DO - 10.1090/S0002-9939-2015-12398-2

M3 - Article

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SN - 0002-9939

VL - 143

SP - 2117

EP - 2128

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -

Brannan’s conjecture and trigonometric sums

Abstract

Keywords

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