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Licensed Unlicensed Requires Authentication Published by De Gruyter July 10, 2012

Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms

  • Roland Matthes EMAIL logo and Yoshinori Mizuno
From the journal Forum Mathematicum


We study some arithmetics of Hermitian modular forms of degree two by applying the spectral theory on 3-dimensional hyperbolic space. This paper presents three main results: (1) a 3-dimensional analogue of Katok–Sarnak's correspondence, (2) an analytic proof of a Hermitian analogue of the Saito–Kurokawa lift by means of a converse theorem, (3) an explicit formula for the Fourier coefficients of a certain Hermitian Eisenstein series.

Funding source: Keio University

Award Identifier / Grant number: 21st Century COE Program

Funding source: Max-Planck-Institut für Mathematik

Funding source: JSPS

Award Identifier / Grant number: Grant-in-Aid for Young Scientists (B) 23740021

The second author would like to thank Professor A. Krieg who kindly answered a question about the generators of Γ0(2)(N). He would also like to thank Professor J. Elstrodt for sending him the article of G. Greefrath. The authors would like to thank the referee for valuable comments and checking many careless presentation.

Received: 2011-10-13
Revised: 2012-3-6
Published Online: 2012-7-10
Published in Print: 2014-11-1

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