New bounds for Gauss sums derived from KTH powers, and for Heilbronn's exponential sum
نویسندگان
چکیده
منابع مشابه
New Bounds for Gauss Sums Derived From k-th Powers, and for Heilbronn’s Exponential Sum
where p is prime, e(x) = exp(2πix), and ep(x) = e(x/p). In each case we shall assume that p | / a unless the contrary is explicitly stated. Gauss sums arise in investigations into Waring’s problem, and other additive problems involving k-th powers. Although they are amongst the simplest complete exponential sums, the question as to their true order of magnitude is far from being resolved. We re...
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where p is a prime power , χ mod p is a Dirichlet character, a, b, n are integers with n ≥ 2. The first sum was studied in connection with Waring’s problem and we have a classical result due to professor Hua [10]. The second sum has not been studied before as far as the authors know. We hope it can be used in the work of generalizing Waring’s problem. In [6], Davenport and Heilbronn showed that...
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The dissertation consists of three articles in which the evaluation of certain exponential sums and Gauss sums and bounds for the absolute values of exponential sums are considered. The summary part of the thesis provides interpretations in terms of coding theory for the results obtained in the articles.
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where p is a prime power with m ≥ 2, χ is a multiplicative character (mod p), epm(·) is the additive character, epm(x) = e 2πix pm , and f, g are rational functions with integer coefficients. It is understood, that the sum is only over values of x for which g and f and both defined as functions on Z/(p), and g is nonzero (mod p). The sum is trivial if f and g are both constants, so we shall alw...
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We show that twisted monomial Gauss sums modulo prime powers can be evaluated explicitly once the power is sufficiently large.
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2000
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qjmath/51.2.221