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Evaluation~ of~ the~ Zeta~ Functions~ of~ Totally~ Real Number Fields and Its Application

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영남수학회 (Youngnam Mathematical Society)|2019.01|East Asian Mathematical Journal|제35권 제1호|pp. 85-90|DOI http://dx.doi.org/10.7858/eamj.2019.011

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참고문헌

키워드

totally real number fieldzeta function.
주제분류수학

초록

In this paper, we are interested in the evaluation of special values of the Dedekind zeta function of a totally real number field. In particular, we revisit Siegel method for values of the zeta function of a totally real number field at negative odd integers and explain how this method is applied to the case of non-normal totally real number field. As one of its applications, we give divisibility property for the values in the special case.

Abstract

In this paper, we are interested in the evaluation of special values of the Dedekind zeta function of a totally real number field. In particular, we revisit Siegel method for values of the zeta function of a totally real number field at negative odd integers and explain how this method is applied to the case of non-normal totally real number field. As one of its applications, we give divisibility property for the values in the special case.

참고문헌 (21)

  1. D. Byeon, "Special values of zeta functions of the simplest cubic fields and their applica-tions", Proc. Japan Acad., Ser. A, 74, pp.13~15 (1998)
  2. J. Browkin, "Tame kernels of cubic cyclic fields", Math. Comp, 74, pp.967~999 (2004)
  3. H. Cohen, "Advanced topics in computational number theory" (2000), Springer
  4. S. J. Cheon, "Evaluation of the Dedekind zeta functions of some non-normal totally real cubic fields at negative odd integers", Manuscripta Math, 124, pp.551~560 (2007)
  5. E. M. Friedlander, "Handbook of K-theory, Vol. 1", pp.139~189 (2005), Springer-Verlag
  6. Paul E, "Evaluation of the Dedekind sums, Eisenstein cocycles, and special values of L-functions", Duke Math, 118(2), pp.229~260 (2003)
  7. U. Halbritter, "On the computation of the values of zeta functions of totally real cubic fields", J. Number Thoery, 36, pp.266~288 (1990)
  8. H. K. Kim, "Values of zeta functions and class number 1 criterion for the simplest cubic fields", Nagoya Math. J, 160, pp.161~180 (2000)
  9. I. Kimura, "Divisibility of orders of K2 groups associated to quadratic fields", Demonstratio Math, 39, pp.277~284 (2006)
  10. H. K. Kim, "Evaluation of zeta function of the simplest cubic field at negative odd integers", Math. Comp, 71, pp.1243~1262 (2002)
  11. J. H. Lee, "Class number one criterion for some non-normal totally real cubic fields", Taiwanese J. Math, 17(3), pp.981~989 (2013)
  12. J. H. Lee, "Evaluation of the Dedekind zeta functions at s =-1 of the simplest quartic elds", J. Number Theory, 143, pp.24~45 (2014)
  13. S. Louboutin, "Algorithmic number theory", pp.318~326 (2004), Springer
  14. B. Mazur, "Class fields of abelian extensions of Q", Invent. Math, 76, pp.179~330 (1984)
  15. P. Ribenboim, "Classical Theory of Algebraic Numbers" (2001), Universitext, Springer-Verlag
  16. J.-P. Serre, "Prospects in mathematics", pp.77~169 (1971), Princeton Univ. Press
  17. T. Shintani, "On evaluation of zeta fucntions of totally real algebraic number fields at non-positive integers", J. Fac. Sci. Univ. Tokyo Sect. IA Math, 23(2), pp.393~417 (1976)
  18. C. L. Siegel, "Berechnung von Zetafuncktionen an ganzzahligen Stellen", Nachr. Akad. Wiss. Gottingen Math.-Phys. Kl, II, pp.87~102 (1969)
  19. E. Tollis, "Zeros of Dedekind zeta functions in the critical strip", Math. Comp, 66(219), pp.1295~1321 (1997)
  20. A. Wiles, "The Iwasawa conjecture for totally real fields", Ann. of Math, 131(2), pp.493~540 (1990)
  21. D. B. Zagier, "On the values at negative integers of the zeta function of a real quadratic eld", Enseignement Math, 22, pp.55~95 (1976)

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