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On positive cosine sums

Published online by Cambridge University Press:  10 April 2007

GAVIN BROWN ,
FENG DAI  and
KUNYANG WANG
GAVIN BROWN
Affiliation:
University of Sydney, Sydney, NSW 2006, Australia. e-mail: vice-chancellor@vcc.usyd.edu.au
FENG DAI
Affiliation:
Department of Mathematical and Statistical Sciences, CAB 632, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1. e-mail: dfeng@math.ualberta.ca
KUNYANG WANG*
Affiliation:
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China. e-mail: wangky@bnu.edu.cn
*
§Corresponding author author KW partially supported by NNSF of China under the grant # 10071007.
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Abstract

For α∈ (0,1) and x∈ [0,π, we define S0(x,α) = 1 and where Also, we set, for α∈ (0,1), where it is agreed that infØ =∞. It is shown in this paper that and 8≤ N(α)<∞ if α0<α<α*, where α*:=0.33542. . . is the unique solution α∈ (0,1) of the equation while α0= 0.308443. . . is the unique solution α∈ (0,1) of the equation In the case α*<α<1, this extends a result of Brown, Wang and Wilson (1993).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 2 , March 2007 , pp. 219 - 232
Copyright
Copyright © Cambridge Philosophical Society 2007

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Footnotes

† Supported by the Australian Research Council.
‡ Partially supported by the NSERC Canada under grant G121211001.

References

REFERENCES

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