Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T07:18:12.213Z Has data issue: false hasContentIssue false
  • English
  • Français

AN EFFECTIVE BOUND FOR THE CYCLOTOMIC LOXTON–KEDLAYA RANK

Published online by Cambridge University Press:  20 March 2017

CONSTANTIN N. BELI ,
FLORIN STAN  and
ALEXANDRU ZAHARESCU
CONSTANTIN N. BELI
Affiliation:
Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit 5, P. O. Box 1-764, RO-014700 Bucharest, Romania e-mails: [email protected], [email protected], [email protected]
FLORIN STAN
Affiliation:
Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit 5, P. O. Box 1-764, RO-014700 Bucharest, Romania e-mails: [email protected], [email protected], [email protected]
ALEXANDRU ZAHARESCU
Affiliation:
Simion Stoilow Institute of Mathematics of the Romanian Academy, Research unit 5, P. O. Box 1-764, RO-014700 Bucharest, Romania Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, IL, 61801, USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we provide an explicit upper bound for the Loxton–Kedlaya rank of the maximal abelian extension of ℚ.

Keywords

11R1811R06
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 97 - 110
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. de Jong, A. J., Smoothness, semi-stability and alterations, Inst. Hautes Études Sci. Publ. Math. 83 (1996), 51–93.CrossRefGoogle Scholar
2. Honda, T., Isogeny classes of abelian varieties over finite fields, J. Math. Soc. Japan 20 (1968), 83–95.CrossRefGoogle Scholar
3. Kronecker, L., Zwei Sätze über Gleichungen mit ganzzahligen Coefficienten, J. Reine Angew. Math. 53 (1857), 173–175.Google Scholar
4. Loxton, J. H., On the maximum modulus of cyclotomic integers, Acta Arith. 22 (1972), 69–85.CrossRefGoogle Scholar
5. Loxton, J. H., On two problems of R. M. Robinson about sums of roots of unity, Acta Arith. 26 (1974/75), 159–174.CrossRefGoogle Scholar
6. Mumford, D., Abelian varieties (Tata Institute of Fundamental Research, Bombay and Oxford University Press, London, 1970).Google Scholar
7. Rosser, J. B. and Schoenfeld, L., Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1) (1962), 64–94.CrossRefGoogle Scholar
8. Stan, F. and Zaharescu, A., Siegel's trace problem and character values of finite groups, J. Reine Angew. Math. 637 (2009), 217–234.Google Scholar
9. Stan, F. and Zaharescu, A., Weil numbers in finite extensions of Qab : The Loxton-Kedlaya phenomenon, Trans. Amer. Math. Soc. 367 (6) (2015), 4359–4376.CrossRefGoogle Scholar
10. Tate, J., Classes d'isogénie de variétés abéliennes sur un corps fini (d'après T. Honda), Exp. No. 352, in Séminaire Bourbaki 1968/69, Lecture Notes in Mathematics 175 (Springer-Verlag, Berlin, 1971), 95–110.Google Scholar