On moduli spaces, equidistribution, estimates, and rational points of algebraic curves

被引：0

作者：

Glazunov N.M. ^{[1
]}

机构：

[1] Institute of Cybernetics, Ukrainian Academy of Sciences, Kiev

来源：

Ukrainian Mathematical Journal | 2001年 / 53卷 / 9期

关键词：

Modulus Space; Rational Point; Finite Field; Algebraic Curf; Hyperelliptic Curve;

D O I：

10.1023/A:1014302305458

中图分类号：

学科分类号：

摘要：

We consider the moduli spaces of hyperelliptic curves, Artin-Schreier coverings, and some other families of curves of this type over fields of characteristic p. By using the Postnikov method, we obtain expressions for the Kloosterman sums. The distribution of angles of the Kloosterman sums was investigated on a computer. For small prime p, we study rational points on curves y2 = f(x). We consider the problem of the accuracy of estimates of the number of rational points of hyperelliptic curves and the existence of rational points of curves of the indicated type on the moduli spaces of these curves over a prime finite field. © 2001 Plenum Publishing Corporation.

引用

页码：1407 / 1418

页数：11

共 20 条

[1]

Harris J., Morrison J., Moduli of Curves, (1998)

[2]

Serre J.-P., Abelian 1 -Adic Representations and Elliptic Curves, (1968)

[3]

Duke W., Friedlander J., Iwaniec H., Bilinear forms with Kloosterman fractions, Invent. Math., 128, pp. 23-33, (1997)

[4]

Livne R., The average distribution of cubic exponential sums, J. Reine Angew. Math., 375, 6, pp. 362-379, (1987)

[5]

Katz N.M., Gauss Sums, Kloosterman Sums, and Monodromy Groups, (1989)

[6]

Linnik Yu. V., Ergodic Properties of Algebraic Fields [in Russian], (1967)

[7]

Adolphson A., On the distribution of angles of Kloosterman sums, J. Reine Angew. Math., 395, pp. 214-220, (1989)

[8]

Glazunov N.M., On distribution and values of Kloosterman sums Tp(c,d) for primes 13499, Representation Theory and Computer Algebra, (1997)

[9]

Gel'fond A.O., Linnik Yu. V., Elementary Methods in Analytic Number Theory [in Russian], (1962)

[10]

Postnikov A.G., Ergodic Problems in the Theory of Congruences and Theory of Diophantine Approximations [in Russian], (1966)

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