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§27.8 Dirichlet Characters… ►An example is the principal character (mod ): … ►Every Dirichlet character (mod ) is a product …A character is real if all its values are real. If is odd, then the real characters (mod ) are the principal character and the quadratic characters described in the next section.
§27.9 Quadratic Characters►For an odd prime , the Legendre symbol is defined as follows. …The Legendre symbol , as a function of , is a Dirichlet character (mod ). … ►If an odd integer has prime factorization , then the Jacobi symbol is defined by , with . The Jacobi symbol is a Dirichlet character (mod ). …
§24.16(ii) Character Analogs►Let be a primitive Dirichlet character (see §27.8). Then is called the conductor of . … ►
6: 25.19 Tables
Fletcher et al. (1962, §22.1) lists many sources for earlier tables of for both real and complex . §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of , and §22.17 lists tables for some Dirichlet -functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.
||stands for any number of alphanumeric characters|
||stands for any zero or one alphanumeric character.|