dirichlet characterとは 意味・読み方・使い方

名詞

Dirichlet character (plural Dirichlet characters)

1. (analytic number theory) A complex-valued arithmetic function ${\\displaystyle \\chi :\\mathbb {Z} \\rightarrow \\mathbb {C} }$ that satisfies the following conditions for some positive integer ${\\displaystyle m}$ and all integers ${\\displaystyle a}$ and ${\\displaystyle b}$:

   1)   ${\\displaystyle \\chi (ab)=\\chi (a)\\chi (b);}$  

   2)   ${\\displaystyle \\chi (a){\\begin{cases}=0&{\\text{if }}\\;\\gcd(a,m)>1\\\\\\neq 0&{\\text{if }}\\;\\gcd(a,m)=1.\\end{cases}}}$text{if }}\\;\\gcd(a,m)=1.\\end{cases}}}"> (gcd is the greatest common divisor)

   3)   ${\\displaystyle \\chi (a+m)=\\chi (a)}$.