The Ramanujan Journal

, Volume 47, Issue 3, pp 475–499 | Cite as

Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series

  • Lynne H. WallingEmail author


We find nice representatives for the 0-dimensional cusps of the degree n Siegel upper half-space under the action of \(\Gamma _0(\mathcal N )\). To each of these, we attach a Siegel Eisenstein series, and then we make explicit a result of Siegel, realizing any integral weight average Siegel theta series of arbitrary level \(\mathcal N \) and Dirichlet character \(\chi _{_L}\) modulo \(\mathcal N \) as a linear combination of Siegel Eisenstein series.


Theta series Quadratic forms Eisenstein series Siegel modular forms 

Mathematics Subject Classification

Primary 11F46 11F11 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK

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