Artin L-Function
An Artin 
-function over the Rationals 
encodes in a Generating Functioninformation about how an irreducible monic Polynomial over 
factors when reduced modulo each Prime. Forthe Polynomial 
, the Artin -function is
where
is a Legendre Symbol, which is equivalent to the Euler L-Function. The definitionover arbitrary Polynomials generalizes the above expression.See also Langlands Reciprocity
References
Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.
- Pythagorean Fraction
- Pythagorean Quadruple
- Pythagorean Square Puzzle
- Pythagorean Theorem
- Pythagorean Triad
- Pythagorean Triangle
- Pythagorean Triple
- Pépin's Test
- Pépin's Theorem
- Pólya-Burnside Lemma
- Pólya Conjecture
- Pólya Distribution
- Pólya Enumeration Theorem
- Pólya Polynomial
- Pólya's Random Walk Constants
- Pólya-Vinogradov Inequality
- Pósa's Theorem
- Q
- q-Analog
- q-Beta Function
- q-Binomial Coefficient
- q-Binomial Theorem
- q-Cosine
- q-Derivative
- q-Dimension