A Quadratic Analogue of Artin's Conjecture on Primitive Roots
A Quadratic Analogue of Artin's Conjecture on Primitive Roots
复制标题
阿廷原根猜想的二次类比
DOI：
10.1006/jnth.1999.2470
复制
发表时间：
2000
影响因子：
0.7
通讯作者：
Hans C. Roskam
中科院分区：
文献类型：
--
作者：
Hans C. Roskam
设e是真实的二次域中的基本单位，S是e具有模p的最大阶的有理素数p的集合。在广义Riemann假设下，证明了S在所有有理素数集合中有密度δ（S）= c · A，其中A为Artin常数，c为正有理数.
Abstract Let e be a fundamental unit in a real quadratic field and let S be the set of rational primes p for which e has maximal order modulo p . Under the assumption of the generalized Riemann hypothesis, we show that S has a density δ ( S )= c · A in the set of all rational primes, where A is Artin's constant and c is a positive rational number.