primitive
♦
7 matching pages ♦
(0.001 seconds)
7 matching pages
1: 27.8 Dirichlet Characters
…
►
27.8.6
►A Dirichlet character is called primitive (mod ) if for every proper divisor of (that is, a divisor ), there exists an integer , with and .
If is prime, then every nonprincipal character is primitive.
…
2: 27.2 Functions
…
►
27.2.1
…
►
27.2.8
►and if is the smallest positive integer such that , then is a primitive root mod .
…
►
27.2.12
…
►
27.2.13
…
3: 27.10 Periodic Number-Theoretic Functions
…
►This is the sum of the th powers of the primitive
th roots of unity.
…
►For a primitive character , is separable for every , and
►
27.10.11
►Conversely, if is separable for every , then is primitive (mod ).
►The finite Fourier expansion of a primitive Dirichlet character has the form
…
4: 27.21 Tables
…
►8 gives examples of primitive roots of all primes ; Table 24.
…
5: 29.17 Other Solutions
…
►They are algebraic functions of , , and , and have primitive period .
…
6: 25.15 Dirichlet -functions
…
►where is a primitive character (mod ) for some positive divisor of (§27.8).
►When is a primitive character (mod ) the -functions satisfy the functional equation:
…
►Since if , (25.15.5) shows that for a primitive character the only zeros of for (the so-called trivial zeros) are as follows:
…