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ℓ-RANKS OF CLASS GROUPS OF FUNCTION FIELDS

정환엽|배성한
대한수학회 (The Korean Mathematical Society)|2012.01|대한수학회지 (Journal of the KMS)|제49권 제1호|pp. 49-67

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참고문헌

키워드

function fieldsclass groups
주제분류수학

초록

In this paper we give asymptotic formulas for the number of ℓ-cyclic extensions of the rational function eld k = Fq(T) with prescribed ℓ-class numbers inside some cyclotomic function elds, and density results for ℓ-cyclic extensions of k with certain properties on the ideal class groups.

Abstract

In this paper we give asymptotic formulas for the number of ℓ-cyclic extensions of the rational function eld k = Fq(T) with prescribed ℓ-class numbers inside some cyclotomic function elds, and density results for ℓ-cyclic extensions of k with certain properties on the ideal class groups.

참고문헌 (13)

  1. B. Angles, "On Hilbert class field towers of global function fields, Drinfeld modules, modular schemes and applications", pp.261~271 (1997), World Sci. Publ
  2. S. Bae, "Genus theory for function fields", J. Austral. Math. Soc. Ser. A, 60(3), pp.301~310 (1996)
  3. A. Frohlich, "Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields" (1983), American Mathematical Society
  4. F. Gerth, "Number fields with prescribed ℓ-class groups", Proc. Amer. Math. Soc, 49, pp.284~288 (1975)
  5. F. Gerth, "Asymptotic behavior of number fields with prescribed ℓ-class numbers", J. Number Theory, 17(2), pp.191~203 (1983)
  6. F. Gerth, "Counting certain number fields with prescribed ℓ-class numbers", J. Reine Angew. Math, 337, pp.195~207 (1982)
  7. F. Gerth, "An application of matrices over finite elds to algebraic number theory", Math. Comp, 41(163), pp.229~234 (1983)
  8. F. Gerth, "The 4-class ranks of quadratic fields", Invent. Math, 77(3), pp.489~515 (1984)
  9. F. Gerth, "Densities for certain ℓ-ranks in cyclic fields of degree ℓn", Compositio Math, 60(3), pp.295~322 (1986)
  10. F. Gerth, "Densities for ranks of certain parts of p-class groups", Proc. Amer. Math. Soc, 99(1), pp.1~8 (1987)
  11. J. Knopfmacher, "Analytic Arithmetic of Algebraic Function Fields" (1979), Marcel Decker Inc
  12. M. Rosen, "Number Theory in Function Fields, GTM vol. 210" (2002), Springer
  13. C. Wittmann, "ℓ-Class groups of cyclic function fields of degree ℓ", Finite Fields Appl, 13(2), pp.327~347 (2007)

관련 논문AI추천

4-RANKS OF CLASS GROUPS OF QUADRATIC EXTENSIONS OF CERTAIN QUADRATIC FUNCTION FIELDS강병련, 배성한대한수학회 · 대한수학회논문집2012 · 제27권 제2호HILBERT ℓ-CLASS FIELD TOWERS OF IMAGINARY ℓ-CYCLIC FUNCTION FIELDS정환엽강원경기수학회 · 한국수학논문집2012 · 제20권 제4호Class number divisibility of quadratic function fields in even characteristic배성한, 정환엽대한수학회 · 대한수학회보2013 · 제50권 제4호Remark on average of class numbers of function fields정환엽강원경기수학회 · 한국수학논문집2013 · 제21권 제4호Cylotomic function fields over finite fields with class number threeDilek Buyruk, Ferruh Ozbudak, Mehpare Bilhan대한수학회 · 대한수학회지2019 · 제56권 제2호Note on average of class numbers of cubic function fields정환엽강원경기수학회 · 한국수학논문집2014 · 제22권 제3호

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