Results 251 to 260 of about 1,085,814 (285)

Linear Codes and Character Sums

COMBINATORICA, 2002
\textit{G. Kalai} and \textit{N. Linial} [IEEE Trans. Inf. Theory 41, 1467-1472 (1995; Zbl 0831.94019)] conjectured that the size of the code with the distribution of distances near the minimal distance is exponentially small. The authors estimate the fraction of non-zero vectors of minimal weights in an \(r\cdot n\)-dimensional subspace of \(\mathbb{Z}
Nathan Linial, Alex Samorodnitsky
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Estimation of a Character Sum

Bulletin of the London Mathematical Society, 1988
The author estimates the sum \[ A=\sum_ ...
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A Class of Character Sums

Journal of the London Mathematical Society, 1971
asterisk (*) meansthat the singularities (modp) of r, and r2 are excluded and in the sum 1 lo (o f 0 (modp)) is to be interpreted as the unique integer w (modp) such that ow = 1 (modp)). Perel'muter has given conditions under which this sum is O(pf), thus generalizing the earlier deep work of Weil [4] and Carlitz and Uchiyama [2].
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Codes and character sums

2006
The proofs of the results of the sections 4 and 5 depend heavily on the deep works of Carlitz and Uchiyama, Deligne, Lang and Weil, and Bombieri, because the essential difficulty was that of estimating an exponential sum. It looks possible that in some cases this difficulty could be avoided by relating the demands of (8) and (9) to the estimate given ...
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SOME CHARACTER SUMS OF THE POLYNOMIALS

JP Journal of Algebra, Number Theory and Applications, 2020
Summary: In this article, we use the analytic methods and the properties of the classical Gauss sums to study the calculating problems of some special character sums of the polynomials with degree \(\geq 4\) and obtain some exact calculating formulae for them.
Zhang, Wenpeng, Zhang, Jiafan
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On a Congruence Related to Character Sums

Canadian Mathematical Bulletin, 1985
AbstractIf χ is a Dirichlet character to a prime-power modulus pα, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the typef(x)g'(x) - f'(x)g(x) ≡ 0(pα),where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ ...
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Mean Values of Character Sums

Canadian Journal of Mathematics, 1979
For a non-principal Dirichlet character χ modulo q,Let the Pólya-Vingradov inequality asserts that M(x) < q1/2 log q see [7]. in the opposite direction it is a trivial consequence of lemma 1 below and 1. Parseval's identity that if χ is primitive modulo q, thenWe show that on average the latter of these estimates is the more precise.THEOREM 1.
Montgomery, H. L., Vaughan, R. C.
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On Double Sums with Multiplicative Characters

Mathematical Notes, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On some elementary character sums

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1998
Let \(p\) be an odd prime and denote by \((\frac *p)\) the Legendre symbol. \textit{R. Tsushima} [Proc. Japan Acad., Ser. A 60, 209-211 (1984; Zbl 0573.10017)] and \textit{K. Hashimoto} [Contemp. Math. 53, 253-276 (1986; Zbl 0592.10024)] found a formula which connects the character sum \[ \sum_{n,m =1}^{p-1} \left( \frac{m-4n}{p} \right) \left( \frac{m}
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On Sums Involving Quadratic Characters

Journal of the London Mathematical Society, 1967
The authors consider the sum \(S(k)=\sum_{n=1}^{p-1}({n\over p})\) where \(p\equiv 3\pmod 4\) and \(({n\over p})\) is Legendre's symbol. Using the theorem of \textit{P. T. Bateman, S. Chowla} and \textit{P. Erdős} [Publ. Math. 1, 165--182 (1950; Zbl 0036.30702)] concerning the size of \(\sum_{n=1}^\infty\frac{({n\over p})}{n}\) the authors show that ...
Ayoub, R. G., Chowla, Sarvadaman, Walum, H.   +2 more
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