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Zeta functions do not determine class numbers
Authors:
Bart de Smit and Robert Perlis
Journal:
Bull. Amer. Math. Soc. 31 (1994), 213-215
MSC:
Primary 11R42; Secondary 11R21, 11R29
MathSciNet review:
1260520
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Abstract: We show that two number fields with the same zeta function, and even with isomorphic adele rings, do not necessarily have the same class number.
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Henri
Cohen, A course in computational algebraic number theory,
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515057 (80c:12014), http://dx.doi.org/10.1016/0022-314X(78)90020-3
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(56 #5503)
- [1]
- H. Cohen, A course in computational number theory, Springer-Verlag, New York, 1993. MR 1228206 (94i:11105)
- [2]
- E. Friedman, Analytic formulas for the regulator of a number field, Invent. Math. 98 (1989), 599-622. MR 1022309 (91c:11061)
- [3]
- R. Perlis, On the class numbers of arithmetically equivalent fields, J. Number Theory 10 (1978), 489-509. MR 515057 (80c:12014)
- [4]
- -, On the equation
 , J. Number Theory 9 (1977), 342-360. MR 0447188 (56:5503)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1994-00520-8
PII:
S 0273-0979(1994)00520-8
Keywords:
Computational number theory,
arithmetic equivalence
Article copyright:
© Copyright 1994 American Mathematical Society
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