Let M(x) be the summatory function of the Mobius function and R(x) be the remainder term for the number of squarefree integers up to x. In this paper, we prove the explicit bounds |M(x)| = 2160535$ and |R(x)| = 438653...
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Let M(x) be the summatory function of the Mobius function and R(x) be the remainder term for the number of squarefree integers up to x. In this paper, we prove the explicit bounds |M(x)| < x/4345 for x >= 2160535$ and |R(x)| <= 0.02767 root x for x >= 438653. These bounds are considerably better than preceding bounds of the same type and can be used to improve Schoenfeld type estimates.
Let R be a complete discrete valuation ring (DVR) of mixed characteristic (0, p) with field of fractions K containing the pth roots of unity. This article is concerned with semistable models of p-cyclic covers of the ...
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Let R be a complete discrete valuation ring (DVR) of mixed characteristic (0, p) with field of fractions K containing the pth roots of unity. This article is concerned with semistable models of p-cyclic covers of the projective line C -> P-K(1). We start by providing a new construction of a semistable model of C in the case of an equidistant branch locus. If the cover is given by the Kummer equation Z(p) = f (X-0), we define what we call the monodromy polynomial L(Y) of f (X-0), a polynomial with coefficients in K. Its zeros are key to obtaining a semistable model of C. As a corollary, we obtain an upper bound for the minimal extension K'/K, over which a stable model of the curve C exists. Consider the polynomial L(Y) Pi(Y-p - f (y(i))), where the yi range over the zeros of L(Y). We show that the splitting field of this polynomial always contains K' and that, in some instances, the two fields are equal.
作者：
Lehr, CMatignon, MUniv Padua
Dipartimento Matemat Pura & Applicata I-35131 Padua Italy Univ Bordeaux 1
UMR 5465 CNRS Lab Theorie Nombres & Algorithm Arithmet F-33405 Talence France
Let k be an algebraically closed field of positive characteristic p > 0 and C -> P-k(1) a p-cyclic cover of the projective line ramified in exactly one point. We are interested in the p-Sylow subgroups of the fu...
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Let k be an algebraically closed field of positive characteristic p > 0 and C -> P-k(1) a p-cyclic cover of the projective line ramified in exactly one point. We are interested in the p-Sylow subgroups of the full automorphism group Aut(k)C. We prove that for curves C with genus 2 or higher, these groups are exactly the extensions of a p-cyclic group by an elementary abelian p-group. The main tool is an efficient algorithm to compute the p-Sylow subgroups of Aut(k)C starting from an Artin-Schreier equation for the cover C -> P-k(1). We also characterize curves C with genus gC >= 2 and a p-group action G subset of Aut(k)C such that 2p/(p-1) < vertical bar G vertical bar/gc and 4/(p-1)(2) <, vertical bar G vertical bar/g(C)(2). Our methods rely on previous work by Stichtenoth whose approach we have adopted.
We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules: we define some zonal functions for the symmetric group and we give ...
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We study (generalized) designs supported by words of given composition. We characterize them in terms of orthogonality relations with Specht modules: we define some zonal functions for the symmetric group and we give a closed formula for them, indexed on ordered pair of semi-standard generalized tableaux: Hahn polynomials are a particular case. We derive an algorithm to test if a set beta is a design. We use it to search designs in some ternary self-dual codes.
作者：
Matignon, MUniv Bordeaux 1
Lab Theorie Nombres & Algorithm Arithmet CNRS UMR 5465 F-33405 Talence France
In his Ph. D. thesis, C. Lehr offers an algorithm which gives the stable model for p-cyclic covers of the projective line over a p-adic field under the conditions that the branch locus whose cardinal is m + 1 has the ...
In his Ph. D. thesis, C. Lehr offers an algorithm which gives the stable model for p-cyclic covers of the projective line over a p-adic field under the conditions that the branch locus whose cardinal is m + 1 has the so called equidistant geometry and m < p. In this note we give an algorithm also in the equidistant geometry case but without condition on m. In particular we are able to study the reduction at 2 of hyperelliptic curves with equidistant branch locus.
Let k be an algebraically closed field of characteristic p > 0. Let m is an element of N, (m, p) = 1. We study F-p-vector spaces of logarithmic differential forms on the projective line such that each non-zero form...
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Let k be an algebraically closed field of characteristic p > 0. Let m is an element of N, (m, p) = 1. We study F-p-vector spaces of logarithmic differential forms on the projective line such that each non-zero form has a unique zero at infinity of given order m - 1. We discuss the existence of such vectors spaces according to the value of in. We give applications to the lifting to characteristic 0 of (Z/pZ)(n) actions as k-automorphisms of k[[t]]. (C) 2002 Elsevier Science (USA).
Using Weil's explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totall...
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Using Weil's explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totally complex fields of degree less than or equal to 30 having the smallest known discriminant.
From recent work of Zhang and of Zagier, we know that their height h(alpha) is bounded away from 1 for every algebraic number alpha different from 0, 1;1/2 +/- root -3/2. The study of the related spectrum is especiall...
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From recent work of Zhang and of Zagier, we know that their height h(alpha) is bounded away from 1 for every algebraic number alpha different from 0, 1;1/2 +/- root -3/2. The study of the related spectrum is especially interesting for it is linked to Lehmer's problem and to a conjecture of Bogomolov. After recalling some definitions, we show an improvement of the so-called Zhang-Zagier inequality. To achieve this, we need some algebraic numbers of small height. So, in the third section, rye describe an algorithm able to find them, and we give an algebraic number with height 1.2875274... discovered in this way. This search up to degree 64 suggests that the spectrum of h(alpha) may have a limit point less than 1.292. We prove this fact in the fourth part.
Integer zeros of binary Krawtchouk polynomials occur in various problems of classical combinatorics. We present some of these properties and generalise them to q-Krawtchouk polynomials. We also give a survey of what i...
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Integer zeros of binary Krawtchouk polynomials occur in various problems of classical combinatorics. We present some of these properties and generalise them to q-Krawtchouk polynomials. We also give a survey of what is known about these zeros. (C) 2001 Academic Press.
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