منابع مشابه
Newton polygons for character sums and Poincaré series
In this paper, we precise the asymptotic behaviour of Newton polygons of L-functions associated to character sums, coming from certain n variable Laurent polynomials. In order to do this, we use the free sum on convex polytopes. This operation allows the determination of the limit of generic Newton polygons for the sum ∆ = ∆1 ⊕ ∆2 when we know the limit of generic Newton polygons for each facto...
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 ...
متن کاملLarge 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 کاملCharacter sums and MacWilliams identities
We show that certain character sums are intimately connected with MacWilliams identities for linear poset codes as well as usual linear codes. We also illustrate in some two poset codes that this method gives much shorter proofs than the ones using discrete Poisson summation formula. © 2004 Elsevier B.V. All rights reserved. MSC: primary 11L03; 94B60; secondary 94B05
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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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2001
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700002421