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Available in print format 		Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Zeta functions do not determine class numbers

Author(s): Bart de Smit; Robert Perlis
Journal: Bull. Amer. Math. Soc. 31 (1994), 213-215.
MathSciNet review: 1260520
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Abstract | References | Additional information

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.

References:

Bibliography

[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 $ {\zeta _K}(s) = {\zeta _{K'}}(s)$, J. Number Theory 9 (1977), 342-360. MR 0447188 (56:5503)

Additional Information:

DOI: 10.1090/S0273-0979-1994-00520-8
PII: S 0273-0979(1994)00520-8
Keywords: Computational number theory, arithmetic equivalence
Copyright of article: Copyright 1994, American Mathematical Society




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