“Siegel Eisenstein series”的意思、由来-开放百科全书

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Siegel Eisenstein series

释义

Definition
Example
See also
References

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.

{{harvtxt|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

References

{{citation|mr=1680317

|last=Katsurada|first= Hidenori
|title=An explicit formula for Siegel series
|journal=Amer. J. Math. |volume=121 |year=1999|issue= 2|pages=415–452|doi=10.1353/ajm.1999.0013|citeseerx=10.1.1.626.6220}}

1 : Automorphic forms

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Definition

Example

See also

References