Frobenius distributions for real quadratic orders
Journal de théorie des nombres de Bordeaux (1995)
- Volume: 7, Issue: 1, page 121-132
- ISSN: 1246-7405
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topStevenhagen, Peter. "Frobenius distributions for real quadratic orders." Journal de théorie des nombres de Bordeaux 7.1 (1995): 121-132. <http://eudml.org/doc/247663>.
@article{Stevenhagen1995,
abstract = {We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.},
author = {Stevenhagen, Peter},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {real quadratic fields; quadratic units; Pell equation; solutions of the Pell equation; integers which are sums of two relatively prime squares; abelian extensions of higher degree},
language = {eng},
number = {1},
pages = {121-132},
publisher = {Université Bordeaux I},
title = {Frobenius distributions for real quadratic orders},
url = {http://eudml.org/doc/247663},
volume = {7},
year = {1995},
}
TY - JOUR
AU - Stevenhagen, Peter
TI - Frobenius distributions for real quadratic orders
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 1
SP - 121
EP - 132
AB - We present a density result for the norm of the fundamental unit in a real quadratic order that follows from an equidistribution assumption for the infinite Frobenius elements in the class groups of these orders.
LA - eng
KW - real quadratic fields; quadratic units; Pell equation; solutions of the Pell equation; integers which are sums of two relatively prime squares; abelian extensions of higher degree
UR - http://eudml.org/doc/247663
ER -
References
top- [1] B.D. Beach and H.C. Williams, A numerical investigation of the Diophantine equation x2 - dy2 = -1, Proc. 3rd Southeastern Conf. on Combinatorics, Graph Theory and Computing, 1972, pp. 37-52. Zbl0261.10015MR347729
- [2] W. Bosma and P. Stevenhagen, Density computations for real quadratic units, Math. Comp., to appear (1995). Zbl0859.11064MR1344607
- [3] H. Cohen and H.W. Lenstra, Jr., Heuristics on class groups of number fields, Number Theory Noordwijkerhout 1983 (H. Jager, ed.), Springer LNM1068, 1984. Zbl0558.12002
- [4] G.H. Hardy and E.M. Wright, An introduction to the theory of numbers, Oxford University Press, 1938. Zbl0020.29201JFM64.0093.03
- [5] T. Nagell, Über die Lösbarkeit der Gleichung x2 - Dy2 = -1, Arkiv för Mat., Astr., o. Fysik23 (1932), no. B/6, 1-5. JFM59.0180.02
- [6] L. Rédei, Über die Pellsche Gleichung t2 - du2 = -1, J. reine angew. Math.173 (1935), 193-221. Zbl0012.24602JFM61.0138.02
- [7] L. Rédei, Über einige Mittelwertfragen im quadratischen Zahlkörper, J. reine angew. Math.174 (1936), 131-148. Zbl0009.29302
- [8] G.J. Rieger, Über die Anzahl der als Summe von zwei Quadraten darstellbaren und in einer primen Restklasse gelegenen Zahlen unterhalb einer positiven Schranke. II, J. reine angew. Math.217 (1965), 200-216. Zbl0141.04305MR174533
- [9] A.J. Stephens and H.C. Williams, Some computational results on a problem of Eisenstein, Théorie des Nombres - Number Theory (J. W. M. de Koninck and C. Levesque, eds. ), de Gruyter, 1992, pp. 869-886. Zbl0689.10024MR1024611
- [10] P. Stevenhagen, On the 2-power divisibility of certain quadratic class numbers, J. of Number Theory43 (1993), no. (1), 1-19. Zbl0767.11054MR1200803
- [11] P. Stevenhagen, The number of real quadratic fields having units of negative norm, Exp. Math.2 (1993), no. (2), 121-136. Zbl0792.11041MR1259426
- [12] P. Stevenhagen, On a problem of Eisenstein, Acta Arith., (to appear, 1995). Zbl0851.11058MR1373712
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