# Mordell-Weil rank of the jacobians of the curves defined by ${y}^{p}=f\left(x\right)$

Acta Arithmetica (1993)

- Volume: 64, Issue: 4, page 297-302
- ISSN: 0065-1036

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topNaoki Murabayashi. "Mordell-Weil rank of the jacobians of the curves defined by $y^p = f(x)$." Acta Arithmetica 64.4 (1993): 297-302. <http://eudml.org/doc/206552>.

@article{NaokiMurabayashi1993,

author = {Naoki Murabayashi},

journal = {Acta Arithmetica},

keywords = {Mordell-Weil rank of the jacobians; superelliptic curves; Mordell-Weil group},

language = {eng},

number = {4},

pages = {297-302},

title = {Mordell-Weil rank of the jacobians of the curves defined by $y^p = f(x)$},

url = {http://eudml.org/doc/206552},

volume = {64},

year = {1993},

}

TY - JOUR

AU - Naoki Murabayashi

TI - Mordell-Weil rank of the jacobians of the curves defined by $y^p = f(x)$

JO - Acta Arithmetica

PY - 1993

VL - 64

IS - 4

SP - 297

EP - 302

LA - eng

KW - Mordell-Weil rank of the jacobians; superelliptic curves; Mordell-Weil group

UR - http://eudml.org/doc/206552

ER -

## References

top- [1] Yu. I. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys 26 (6) (1971), 7-78. Zbl0266.14012
- [2] B. Mazur, Rational points of abelian varieties with values in towers of number fields, Invent. Math. 18 (1972), 183-266. Zbl0245.14015
- [3] H. P. F. Swinnerton-Dyer, The conjectures of Birch and Swinnerton-Dyer, and of Tate, in: Proceedings of a conference on local fields (Driebergen, 1966), Springer, 1967, 132-157.
- [4] J. Top, A remark on the rank of jacobians of hyperelliptic curves over ℚ over certain elementary abelian 2-extensions, Tôhoku Math. J. 40 (1988), 613-616. Zbl0688.14027
- [5] A. Weil, Jacobi sums as Grössencharaktere, Trans. Amer. Math. Soc. 73 (1952), 487-495. Zbl0048.27001

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