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Asymptotic evaluation of Gauss polynomials


Authors: Patrick X. Gallagher, L. Thomas Ramsey and Benjamin B. Wells
Journal: Proc. Amer. Math. Soc. 86 (1982), 15-18
MSC: Primary 10G10
DOI: https://doi.org/10.1090/S0002-9939-1982-0663856-2
MathSciNet review: 663856
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Abstract: An asymptotic evaluation is given for the polynomials $ G(\alpha ) = \sum\nolimits_{j = 1}^n {e({j^2}/n)e(j\alpha )} $ for $ 4\vert n$.


References [Enhancements On Off] (What's this?)

  • [1] J. S. Byrnes, On the polynomials with coefficients of modulus one, Bull. London Math. Soc. 9 (1977), 171-176. MR 0486435 (58:6181)
  • [2] P. G. Lejeune Dirichlet, Vorlesungen über Zahlentheorie, F. Vieweg Braunschweig, 1894.
  • [3] J.-P. Kahane, Sur les polynomes $ \Sigma \exp (i{\theta _m}){Z^m}$ (preprint).
  • [4] J. E. Littlewood, On the mean values of certain trigonometrical polynomials. II, Illinois J. Math. 6 (1962), 1-39. MR 0141935 (25:5331b)

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DOI: https://doi.org/10.1090/S0002-9939-1982-0663856-2
Article copyright: © Copyright 1982 American Mathematical Society

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