Iwasawa invariants and class numbers

of quadratic fields for the prime

Author:
Hisao Taya

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1285-1292

MSC (1991):
Primary 11R23, 11R11, 11R29

DOI:
https://doi.org/10.1090/S0002-9939-99-05177-1

Published electronically:
August 3, 1999

MathSciNet review:
1641133

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a square-free integer with and . Put and . For the cyclotomic -extension of , we denote by the -th layer of over . We prove that the -Sylow subgroup of the ideal class group of is trivial for all integers if and only if the class number of is not divisible by the prime . This enables us to show that there exist infinitely many real quadratic fields in which splits and whose Iwasawa -invariant vanishes.

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Additional Information

**Hisao Taya**

Email:
taya@math.is.tohoku.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-05177-1

Keywords:
Iwasawa invariants,
real quadratic fields,
class numbers

Received by editor(s):
August 27, 1997

Received by editor(s) in revised form:
June 22, 1998

Published electronically:
August 3, 1999

Additional Notes:
This research was partially supported by the Grant-in-Aid for Encouragement of Young Scientists, The Ministry of Education, Science, Sports and Culture, Japan.

Dedicated:
Dedicated to Professor Koji Uchida on his 60th birthday

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2000
American Mathematical Society