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On the Distribution of Integral Ideals and Hecke Grssencharacters

On the Distribution of Integral Ideals and Hecke Grssencharacters
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摘要 The author uses analytic methods to study the distribution of integral ideals and Hecke Grssencharacters in algebraic number fields. Nowak’s results on the distribution of integral ideals, and Chandrasekharan and Good’s results on the distribution of Hecke Grssencharacters are improved. The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and Good＇s results on the distribution of Hecke GrSssencharacters are improved.
作者 Huixue LAO
机构地区 School of Mathematical Sciences
出处 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第3期385-392,共8页 数学年刊（B辑英文版）
基金 Project supported by the National Natural Science Foundation of China (Nos. 10701048, 10971119) the Shandong Provincial Natural Science Foundation of China (No. ZR2009AQ007)
关键词 理想分布 积分 代数数域 Dedekind zeta-function, Integral ideal, Grossencharacters
分类号 O172.2 [理学—基础数学] X145 [环境科学与工程—环境科学]
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参考文献10

  • 1Weber, H., Lehrbuch der Algebra, Vol. Ⅱ, Vieweg, Braunschweig, 1896.
  • 2Landau, E., Einfuhrung in die Elementare umd Analytische Theorie der Algebraischen Zahlen und der Ideals, Chelsea, New York, 1949.
  • 3Huxley, M. N. and Watt, N., The number of ideals in a quadratic field Ⅱ, Israel J. Math. Part A, 120, 2000, 125-153.
  • 4Miiller, W., On the distribution of ideals in cubic number fields, Monatsh. Math., 106, 1988, 211-219.
  • 5Nowak, W. G., On the distribution of integral ideals in algebraic number theory fields, Math. Nachr., 161, 1993, 59-74.
  • 6Chandraseknaran, K. and Narasimhan, R., Functional equations with mutiple Gamma factors and the average order of arithmetical functions, Ann. of Math., 76, 1962, 93-136.
  • 7Iwaniec, H. and Kowalski, E., Analytic Number Theory, Colloquium Publications, Vol. 53, A. M. S., Providence, RI, 2004.
  • 8Heath-Brown, D. R., The growth rate of the Dedekind zeta-function on the critical line, Acta Arith., 49, 1988, 323-339.
  • 9Sohne, P., An upper bound for Hecke zeta-functions with Grossencharacters, J. Number Theory, 66, 1997, 225-250.
  • 10Chandraseknaran, K. and Good, A., On the number of integeral ideals in Galois extensions, Monatsh. Math., 95, 1983, 99-109.
Chinese Annals of Mathematics,Series B
2010年 第3期

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