Ralf Schmidt

Ralf Schmidt
University of Oklahoma
Department of Mathematics
Norman, OK 73019-3103
Phone:	405-325-3684
E-mail:	rschmidt...math.ou.edu
Office:	PHSC 814

Research Interests

Classical and adelic modular forms
Local and global representation theory
Automorphic L-functions

Click here for our Representation Theory Seminar

Course Information for Students

Math 2443 (Spring 2012)
Local Class Field Theory (Spring 2012)

TORA

Texas-Oklahoma Representations and Automorphic Forms is a new regional conference series organized jointly by UNT, OSU and OU and supported by NSF grants DMS-1132586 and DMS-1132510. The first meeting, TORA I, was held September 17-18, 2011, at UNT, and TORA II was held April 6-8, 2012, at OSU. TORA III is planned for September 28-30 at OU. The predecessor to the TORA conference series was this event.

Selected Publications and Preprints

Local Newforms for GSp(4) and the Metaplectic Group

All of the following material is collaborative work with Brooks Roberts.

New vectors for GSp(4): a conjecture and some evidence.
Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 107-121
pdf proceedings
On modular forms for the paramodular group.
In: Automorphic Forms and Zeta Functions. Proceedings of the Conference in Memory of Tsuneo Arakawa. World Scientific, 2006
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Local Newforms for GSp(4).
Springer Lecture Note in Mathematics, vol. 1918 (2007)
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An alternative proof of a theorem on local newforms for GSp(4).
Proceedings of the 9th Autumn Workshop on Number Theory, Hakuba, Japan, 2006
pdf conference web page
A decomposition of the spaces $S_k(\Gamma_0(N))$ in degree 2 and the construction of hypercuspidal modular forms.
Proceedings of the 9th Autumn Workshop on Number Theory, Hakuba, Japan, 2006
pdf conference web page
Tables for Representations of GSp(4).
These are several tables containing information on the p-adic representation theory of the group GSp(4). Feel free to use the tables if you need them.
pdf latex
On the number of local newforms in a metaplectic representation.
In: Arithmetic Geometry and Automorphic Forms, International Press and Higher Education Press, 2011
pdf

Bessel Models and Integral Representations for GSp(4) x GL(2)

Joint with Ameya Pitale: Bessel models for lowest weight representations of GSp(4,R).
Int. Math. Res. Not. 2009, 1159-1212
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Joint with Ameya Pitale: Integral representation for L-functions for GSp(4) x GL(2).
J. Number Theory 129 (2009), 1272-1324
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Joint with Ameya Pitale and Abhishek Saha: Transfer of Siegel cusp forms of degree 2.
Preprint, 2011
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Saito-Kurokawa and Ikeda Lifting

On the spin L-function of Ikeda's lifts.
Comment. Math. Univ. St. Paul 52 (2003), 1-46
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The Saito-Kurokawa lifting and functoriality.
Amer. J. Math. 127 (2005), 209-240
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On classical Saito-Kurokawa liftings.
J. Reine Angew. Math. 604 (2007), 211-236
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Siegel Modular Forms of Degree 2

On Siegel modular forms of degree 2 with square-free level.
Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 155-169
pdf proceedings
Iwahori-spherical representations of GSp(2) and Siegel modular forms of degree 2 with square-free level.
J. Math. Soc. Japan 57 (2005), 259-293
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Joint with Ameya Pitale: Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2.
Proc. Amer. Math. Soc. 136 (2008), 3831-3838
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Joint with Ameya Pitale: Ramanujan-type results for Siegel cusp forms of degree 2.
J. Ramanujan Math. Soc. 24 (2009), 87-111
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A remark on a paper of Ibukiyama and Skoruppa.
Abh. Math. Sem. Univ. Hamburg 79 (2009), 189-191
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Joint with Abhishek Saha: Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions.
Preprint, 2011
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Other

Joint with Mahdi Asgari: Siegel modular forms and representations.
Manuscripta Math. 104 (2001), 173-200
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Some remarks on local newforms for GL(2).
J. Ramanujan Math. Soc. 17 (2002), 115-147
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On the archimedean Euler factors for spin L-functions.
Abh. Math. Sem. Univ. Hamburg 72 (2002), 119-143
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Joint with Mahdi Asgari: On the adjoint L-function of the p-adic GSp(4).
J. Number Theory 128 (2008), 2340-2358
pdf

gsp4.org

gsp4.org is a website established in collaboration with Brooks Roberts and supported through NSF grants #0454809 and #0400837 and by the Department of Mathematics of the University of Oklahoma. Its goal is to provide bibliographical information on the existing literature on GSp(4), including all aspects of the representation theory of this group and related topics like Siegel modular forms of degree two. The database was opened to the public on Feb. 14, 2007, at which point it contained 1262 articles and books.

If you have material which you think should be listed on gsp4.org, please let us know. We welcome any comments.

Other Material

The Sato-Tate Pages. An easy introduction to the Sato-Tate conjecture, created in collaboration with Julian Rosen. Contains some historical remarks.
Lineare Algebra (Sorry, this is in German.)
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I am the webmaster for the math department. For any Internet related questions, I recommend this tutorial. You might also want to watch this instructional video.