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Euler L-Function


A special case of the Artin L-function for the polynomial x^2+1. It is given by

 L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)),
(1)

where

chi^-(p)={1 for p=1 (mod 4); -1 for p=3 (mod 4)
(2)
=((-1)/p),
(3)

where (-1/p) is a Legendre symbol.


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References

Knapp, A. W. "Group Representations and Harmonic Analysis, Part II." Not. Amer. Math. Soc. 43, 537-549, 1996.

Referenced on Wolfram|Alpha

Euler L-Function

Cite this as:

Weisstein, Eric W. "Euler L-Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EulerL-Function.html

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