منابع مشابه
Large Character Sums
where χ is a non-principal Dirichlet character χ (mod q). It is easy to show that such character sums are always ≤ q in absolute value, while G. Pólya and I.M. Vinogradov (see [3]) improved this to≤ √q log q around 1919, and H.L. Montgomery and R.C. Vaughan [13] to √q log log q in 1977, assuming the Generalized Riemann Hypothesis (GRH). Up to the constant this is “best possible” since R.E.A.C. ...
متن کاملHermite Character Sums
This evaluation proves a conjecture in [9, p. 370] and solves the problem of finding explicitly the number of rational points (mod/?) on the surface z = (x + l)(y + ΐ)(x + y), a problem some algebraic geometers had worked on without success. Character sum analogues of the important formulas for orthogonal polynomials are potentially as useful as those for hypergeometric series, so a systematic ...
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In this article, the properties of character sums, including Gauss sums and Jacobi sums are investigated.
متن کامل2 3 M ar 1 99 9 LARGE CHARACTER SUMS
where χ is a non-principal Dirichlet character χ (mod q). It is easy to show that such characters sums are always ≤ q in absolute value, while G. Pólya and I.M. Vinogradov [3] improved this to ≤ √q log q around 1919, and H.L. Montgomery and R.C. Vaughan [13] to ≪ √q log log q assuming the Generalized Riemann Hypothesis (GRH), in 1977. Up to the constant this is “best possible” since R.E.A.C. Pa...
متن کاملLinear Codes and Character Sums
Let V be an rn-dimensional linear subspace of Zn 2 . Suppose the smallest Hamming weight of non-zero vectors in V is d. (In coding-theoretic terminology, V is a linear code of length n, rate r and distance d.) We settle two extremal problems on such spaces. First we prove a (weak form) of a conjecture by Kalai and Linial and show that the fraction of vectors in V with weight d is exponentially ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1995
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1097