Minimum of quadratic forms with respect to Fuchsian groups. I.
Minimum of quadratic forms with respect to Fuchsian groups. I.
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Fuchsian 群的最小二次形式。
DOI：
10.1515/crll.1976.286-287.341
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
Asmus L. Schmidt
中科院分区：
文献类型：
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作者：
Asmus L. Schmidt
其中e {1，2，5，. . .}出现在满足马尔可夫方程（1.2）的三元组（x^，x 2，x 3）中。马可夫[15]（另见L。E. Dickson [6]）使用正则连分式，并且马尔可夫形式以1-1对应于所谓的马尔可夫符号来构造。G，Frobenius [10]，R. [18]，[19]，and J. W. S. Cassels [1]使用隔离定理和二次型的紧致性论证。这里，马尔可夫形式的构造基于（1）的解。2）。第三种方法由于H.科恩[2]（见C。G. Lekkerkerker [13]）将马尔可夫形式的构造与亏格1的特定模群的生成元的某些三元组联系起来。该方法充分利用了R. [8]：（1. 3)（trT（l . 4)tr UTU + tr T =（tr U）（tr TU），对行列式l的任何（真实的）2 x 2矩阵T，U有效。
where e {l, 2, 5, . . .} occur in triples (x^, x2, x3) satisfying Markoffs equation (1.2) The proof by A. Markoff [15] (see also L. E. Dickson [6]) uses regulär continued fractions, and the Markoff forms are constructed in 1-1 correspondance to the so-called Markoffsymbols. Another method of proof due to G, Frobenius [10], R. Remak [18], [19], and J. W. S. Cassels [1] works with Isolation theorems and compactness arguments for quadratic forms. The construction of the Markoff forms is here based on the Solutions of (1. 2). A third approach due to H. Cohn [2] (see also C. G. Lekkerkerker [13]) relates the construction of the Markoff forms to certain triples of generators of a specific modular group of genus 1. This method makes essential applications of the following trace relations of R. Fricke [8] : (1. 3) (trT (l . 4) tr UTU + tr T = (tr U) (tr TU), valid for any (real) 2 x 2 matrices T, U of determinant l.)