# A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms

Acta Arithmetica (1999)

- Volume: 89, Issue: 3, page 295-299
- ISSN: 0065-1036

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top## How to cite

topDongho Byeon. "A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms." Acta Arithmetica 89.3 (1999): 295-299. <http://eudml.org/doc/207272>.

@article{DonghoByeon1999,

author = {Dongho Byeon},

journal = {Acta Arithmetica},

keywords = {Iwasawa invariant; imaginary quadratic field; modular forms},

language = {eng},

number = {3},

pages = {295-299},

title = {A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms},

url = {http://eudml.org/doc/207272},

volume = {89},

year = {1999},

}

TY - JOUR

AU - Dongho Byeon

TI - A note on basic Iwasawa λ-invariants of imaginary quadratic fields and congruence of modular forms

JO - Acta Arithmetica

PY - 1999

VL - 89

IS - 3

SP - 295

EP - 299

LA - eng

KW - Iwasawa invariant; imaginary quadratic field; modular forms

UR - http://eudml.org/doc/207272

ER -

## References

top- [1] H. Cohen, A Course in Computational Algebraic Number Theory, Grad. Texts in Math. 138, Springer, New York, 1995.
- [2] H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields II, Proc. Roy. Soc. London Ser. A 322 (1971), 405-420. Zbl0212.08101
- [3] P. Hartung, Proof of the existence of infinitely many imaginary quadratic fields whose class number is not divisible by 3, J. Number Theory 6 (1974), 276-278. Zbl0317.12003
- [4] K. Horie, A note on basic Iwasawa λ-invariants of imaginary quadratic fields, Invent. Math. 88 (1987), 31-38.
- [5] K. Horie and Y. Onishi, The existence of certain infinite families of imaginary quadratic fields, J. Reine Angew. Math. 390 (1988), 97-113. Zbl0638.12001
- [6] K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258. Zbl0074.03002
- [7] W. Kohnen and K. Ono, Indivisibility of class numbers of imaginary quadratic fields and orders of Tate-Shafarevich groups of elliptic curves with complex multiplication, Invent. Math. 135 (1999), 387-398. Zbl0931.11044
- [8] J. Nakagawa and K. Horie, Elliptic curves with no rational points, Proc. Amer. Math. Soc. 104 (1988), 20-24. Zbl0663.14023
- [9] K. Ono, Indivisibility of class numbers of real quadratic fields, Compositio Math., to appear. Zbl1002.11080
- [10] G. Shimura, On modular forms of half-integral weight, Ann. of Math. 97 (1973), 440-481. Zbl0266.10022
- [11] J. Sturm, On the congruence of modular forms, in: Lecture Notes in Math. 1240, Springer, 1984, 275-280.
- [12] H. Taya, Iwasawa invariants and class numbers of quadratic fields for the prime 3, Proc. Amer. Math. Soc., to appear. Zbl0958.11069

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