Siegel Eisenstein series
In mathematics, a Siegel Eisenstein series (sometimes just called an Eisenstein series or a Siegel series) is a generalization of Eisenstein series to Siegel modular forms.
Katsurada (1999) gave an explicit formula for their coefficients.
Definition
The Siegel Eisenstein series of degree g and weight an even integer k > 2 is given by the sum
Sometimes the series is multiplied by a constant so that the constant term of the Fourier expansion is 1.
Here Z is an element of the Siegel upper half space of degree d, and the sum is over equivalence classes of matrices C,D that are the "bottom half" of an element of the Siegel modular group.
Example
gollark: Authoritarian systems tend to lead to a lot of inequality too, which you seem to dislike.
gollark: Wait, so you're against monopolies but for authoritarian governments?
gollark: Probably money, if there's some sort of ridiculous conspiracy to make North Korea look bad.
gollark: I am *not*, since going around punishing for speech (except in rare cases of direct harm) is a very problematic and slippery slope.
gollark: If you give governments or whoever the power to go around getting rid of speech *you* don't like, they can happily proceed to do it to speech you like too.
See also
- Klingen Eisenstein series, a generalization of the Siegel Eisenstein series.
References
- Katsurada, Hidenori (1999), "An explicit formula for Siegel series", Amer. J. Math., 121 (2): 415–452, CiteSeerX 10.1.1.626.6220, doi:10.1353/ajm.1999.0013, MR 1680317
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