منابع مشابه
The least k-th power non-residue
Let p be a prime number and let k ≥ 2 be an integer such that k divides p − 1. Norton proved that the least k-th power non-residue modp is at most 3.9p log p unless k = 2 and p ≡ 3 (mod 4), in which case the bound is 4.7p log p. With a combinatorial idea and a little help from computing power, we improve the upper bounds to 0.9p log p and 1.1p log p, respectively.
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In this paper, we study explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression. We also refine the classical conditional bounds of Littlewood for L-functions at s = 1. In part...
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This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic non-residue and the least prime in an arithmetic progression. We also refine the classical conditional bounds of Littlewood for L-functions at s = 1. In particula...
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• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...
متن کاملLong Quadratic Residue Codes
A long standing problem has been to develop “good” binary linear block codes, C, to be used for error-correction. The length of the block is denoted n and the dimension of the code is denoted k. So in this notation C ⊆ GF (2) is a k-dimensional subspace. Another important parameter is the smallest weight of any non-zero codeword, d. This is related to error-correction because C can correct [d−1...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2008
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042108001432