Periodic points of algebraic functions related to a continued fraction of Ramanujan

被引:0
作者
Akkarapakam, Sushmanth J. [1 ]
Morton, Patrick [2 ]
机构
[1] Univ Missouri Columbia, Dept Math, 208 Math Sci Bldg,810 Rollins St, Columbia, MO 65211 USA
[2] Indiana Univ Purdue Univ Indianapolis IUPUI, Dept Math Sci, 402 N Blackford St,LD 270, Indianapolis, IN 46202 USA
来源
NEW YORK JOURNAL OF MATHEMATICS | 2024年 / 30卷
关键词
Periodic points; algebraic function; 2-adic field; extended ring class fields; Ramanujan continued fraction; DIOPHANTINE EQUATIONS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A continued fraction nu(tau) of Ramanujan is evaluated at certain arguments in the field K = Q(v-d), with -d 1 (mod 8), in which the ideal (2) = (sic)(2) (sic)(2)' is a product of two prime ideals. These values of nu(tau) are shown to generate the inertia field of (sic)(2)or (sic)(2)' in an extended ring class field over the field K. The conjugates over Q of these same values, together with 0, -1 +/-root 2, are shown to form the exact set of periodic points of a fixed algebraic function F(sic)(x), independent of d. These are analogues of similar results for the Rogers-Ramanujan continued fraction.
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页码:783 / 827
页数:45
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