# Densities for certain $l$-ranks in cyclic fields of degree ${l}^{n}$

Compositio Mathematica (1986)

- Volume: 60, Issue: 3, page 295-322
- ISSN: 0010-437X

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topGerth, III, Frank. "Densities for certain $l$-ranks in cyclic fields of degree $l^n$." Compositio Mathematica 60.3 (1986): 295-322. <http://eudml.org/doc/89810>.

@article{Gerth1986,

author = {Gerth, III, Frank},

journal = {Compositio Mathematica},

keywords = {-class rank; cyclic extension; genus group},

language = {eng},

number = {3},

pages = {295-322},

publisher = {Martinus Nijhoff Publishers},

title = {Densities for certain $l$-ranks in cyclic fields of degree $l^n$},

url = {http://eudml.org/doc/89810},

volume = {60},

year = {1986},

}

TY - JOUR

AU - Gerth, III, Frank

TI - Densities for certain $l$-ranks in cyclic fields of degree $l^n$

JO - Compositio Mathematica

PY - 1986

PB - Martinus Nijhoff Publishers

VL - 60

IS - 3

SP - 295

EP - 322

LA - eng

KW - -class rank; cyclic extension; genus group

UR - http://eudml.org/doc/89810

ER -

## References

top- [1] H. Cohen and H. Lenstra, Jr.: Heuristics on class groups of number fields. Lecture Notes in Math.1068 (1984) 33-62. Zbl0558.12002MR756082
- [2] A. Fröhlich: Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields. American Mathematical Society, Providence, R.I. (1983). Zbl0519.12001MR720859
- [3] F. Gerth: Counting certain number fields with prescribed l-class numbers, J. Reine Angew. Math.337 (1982) 195-207. Zbl0485.12006MR676052
- [4] F. Gerth: An application of matrices over finite fields to algebraic number theory. Math. Comp.41 (1983) 229-234. Zbl0519.12003MR701637
- [5] F. Gerth: The 4-class ranks of quadratic fields. Invent. Math.77 (1984) 489-515. Zbl0533.12004MR759260
- [6] F. Gerth: Densities for ranks of certain parts of p-class groups, to appear. Zbl0625.12005MR866419
- [7] G. Hardy and E. Wright: An Introduction to the Theory of Numbers, 4th ed. Oxford Univ. Press, London (1965). Zbl0020.29201MR568909
- [8] G. Landsberg: Über eine Anzahlbestimmung und eine damit zusammenhängende Reihe. J. Reine Angew. Math.111 (1893) 87-88. Zbl25.0430.01JFM25.0430.01
- [9] P. Morton: Density results for the 2-classgroups of imaginary quadratic fields. J. Reine Angew. Math.332 (1982) 156-187. Zbl0491.12004MR656862

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