๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Some formulas concerning the fundamental unit of a real quadratic field

โœ Scribed by H.C. Williams

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
501 KB
Volume
92
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Williams, H.C., Some formulas concerning the fundamental unit of a real quadratic field, Discrete Mathematics 92 (1991) 431-440. Let E be the fundamental unit of a real quadratic field of discriminant d and let integers V, and U" be defined by (V" + u&ii/2 = &". It is well known that it p is any odd prime, then p 1 U,,,, where m =p -x and x is the value of the Legendre symbol (d/p). In this paper several formulas are derived for the value of CJJp (modp) for the case in which p i d. 1. IntcotIuction Let E = (V + Ufi)/2 be the fundamental unit of the real quadratic field X with fundamental discriminant d and define integers V,, U, by V,Hlti 2" =(V+;~)"_ U-1) * Research supported by NSERC of Canada grant #A7649.

๐Ÿ“œ SIMILAR VOLUMES

Explicit Representation of Fundamental U
Explicit Representation of Fundamental Units of Some Real Quadratic Fields, II
โœ Koshi Tomita ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 321 KB

In the preceding paper, (K. Tomita, Proc. Japan Acad. Ser. A Sci. Math. 71 (1995), 41 43), for all real quadratic fields Q(-d ) such that the period k d of the continued fraction expansion of d) and d itself by using two parameters appearing in the continued fraction expansion of | d ; In this paper