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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On values of exponential sums
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by Chungming An PDF
Proc. Amer. Math. Soc. 52 (1975), 131-135 Request permission

Abstract:

An exponential sum is defined by \[ G(F,\varphi ,\alpha ) = \sum \limits _{\gamma \epsilon {{(Z/qZ)}^n}} {\exp (2\pi i(\varphi F(\gamma ) + \langle \alpha ,\gamma \rangle } ))\] for $\varphi = a/q\epsilon Q,\alpha \epsilon {R^n}$, and a positive-definite form $F(x)$ in $n$ variables of degree $\delta$. Its value is studied and the definition is extended to an irrational $\varphi$.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 131-135
  • MSC: Primary 10H10; Secondary 10G05
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0376561-3
  • MathSciNet review: 0376561