منابع مشابه
Explicit evaluation of some exponential sums
Let m be a positive integer, let r be a prime such that 2 is a primitive root modulo r, and let q = 2(r−1)r m−1 . In this note a binomial exponential sum over Fq which assumes 3 2 log2 q + 2 distinct values is explicitly evaluated and its value distribution is determined.
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where the implied constant is absolute. This is proved in [1, §13, 14] (see also [5, Th. 11.42] for an outline of the proof). In this note, we sketch a different proof, based on the general philosophy of reduction to one-variable sums and on the use of the powerful form of Deligne’s proof of the Riemann Hypothesis over finite fields involving sums of trace functions of general sheaves [3] (see ...
متن کاملOn some congruence with application to exponential sums
We will study the solution of a congruence, x ≡ g(1/2)ωg(2 n) mod 2n, depending on the integers g and n, where ωg(2) denotes the order of g modulo 2n. Moreover, we introduce an application of the above result to the study of an estimation of exponential sums.
متن کاملA note on evaluations of some exponential sums
where χ is a non-trivial additive character of the finite field Fq, q = p odd, and a ∈ Fq . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of p+1. The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to ev...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1948
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.34.5.204