Proceedings of the American Mathematical Society

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



On values of exponential sums

Author: Chungming An
Journal: Proc. Amer. Math. Soc. 52 (1975), 131-135
MSC: Primary 10H10; Secondary 10G05
MathSciNet review: 0376561
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Abstract: An exponential sum is defined by

$\displaystyle G(F,\varphi ,\alpha ) = \sum\limits_{\gamma \epsilon {{(Z/qZ)}^n}} {\exp (2\pi i(\varphi F(\gamma ) + \langle \alpha ,\gamma \rangle } ))$

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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Article copyright: © Copyright 1975 American Mathematical Society