Research Interests
 Classical and adelic modular forms
 Local and global representation theory
 Automorphic Lfunctions

Course Information for Students
TORA
TexasOklahoma Representations and Automorphic Forms is a regional conference series organized jointly by
UNT,
OSU and
OU. So far, six TORA meetings took place:
 TORA I, September 1718, 2011, at UNT
 TORA II, April 68, 2012, at OSU
 TORA III, September 2830, 2012, at OU
 TORA IV, March 2324, 2013, at UNT
 TORA V, September 2022, 2013, at OSU
 TORA VI, March 79, 2014, at OU
 TORAS I (student TORA), March 2829, 2015, at OU
TORA is made possible by grants from the NSF. The OU meetings were supported by NSF grants
DMS1132510 and
DMS1302751.
The predecessor to the TORA conference series was
this event. The next meeting is
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), 107121

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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

pdf

Local Newforms for GSp(4).

Springer Lecture Note in Mathematics, vol. 1918 (2007)

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errata

An alternative proof of a theorem on local newforms for GSp(4).

Proceedings of the 9th Autumn Workshop on Number Theory, Hakuba, Japan, 2006

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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

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Tables for Representations of GSp(4).

These are several tables containing information on the padic representation theory of the group GSp(4).
Feel free to use the tables if you need them.

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latex

On the number of local newforms in a metaplectic representation.

In: Arithmetic Geometry and Automorphic Forms, International Press and Higher Education Press, 2011

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Some remarks on Bessel functionals for GSp(4).

Documenta Math. 21 (2016), 467553

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

On the spin Lfunction of Ikeda's lifts.

Comment. Math. Univ. St. Paul 52 (2003), 146

pdf

The SaitoKurokawa lifting and functoriality.

Amer. J. Math. 127 (2005), 209240

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On classical SaitoKurokawa liftings.

J. Reine Angew. Math. 604 (2007), 211236

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Joint with David Farmer, Ameya Pitale and Nathan Ryan:
Survey article: Characterizations of the SaitoKurokawa lifting.

Rocky Mountain J. Math. 43 (2013), 17471757

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Joint with Ameya Pitale and Abhishek Saha:
Local and global Maass relations.

Preprint, 2013

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expanded version
Siegel Modular Forms of Degree 2

On Siegel modular forms of degree 2 with squarefree level.

Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 155169

pdf
proceedings

Iwahorispherical representations of GSp(2) and Siegel modular forms of degree 2 with squarefree level.

J. Math. Soc. Japan 57 (2005), 259293

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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), 38313838

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Joint with Ameya Pitale:
Ramanujantype results for Siegel cusp forms of degree 2.

J. Ramanujan Math. Soc. 24 (2009), 87111

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A remark on a paper of Ibukiyama and Skoruppa.

Abh. Math. Sem. Univ. Hamburg 79 (2009), 189191

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Joint with David Farmer and Nathan Ryan:
Testing the functional equation of a highdegree Euler product.

Pacific J. Math 253 (2011), 349366

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Joint with Abhishek Saha:
Yoshida lifts and simultaneous nonvanishing of dihedral twists of modular Lfunctions.

J. Lond. Math. Soc. 88 (2013), 251–270

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Joint with Ameya Pitale and Abhishek Saha:
Lowest weight modules of Sp_4(R) and nearly holomorphic Siegel modular forms.

Preprint, 2015

arXiv

Joint with Ameya Pitale and Abhishek Saha:
Representations of SL_2(R) and nearly holomorphic modular forms.

Preprint, 2015
(This note may be viewed as an introduction to the previous paper.)

arXiv

Archimedean aspects of Siegel modular forms of degree 2.

Preprint, 2015

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Packet structure and paramodular forms.

Preprint, 2016

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Other

Joint with Mahdi Asgari:
Siegel modular forms and representations.

Manuscripta Math. 104 (2001), 173200

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Some remarks on local newforms for GL(2).

J. Ramanujan Math. Soc. 17 (2002), 115147

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On the archimedean Euler factors for spin Lfunctions.

Abh. Math. Sem. Univ. Hamburg 72 (2002), 119143

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Joint with Mahdi Asgari:
On the adjoint Lfunction of the padic GSp(4).

J. Number Theory 128 (2008), 23402358

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Joint with HiroAki Narita and Ameya Pitale:
Irreducibility criteria for local and global representations.

Proc. Amer. Math. Soc. 141 (2013), 55–63

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Other Material

The SatoTate Pages. An easy introduction to the SatoTate conjecture, created in collaboration with Julian Rosen. Contains some historical remarks.

I used to be the webmaster for the math department. For any Internet related questions, I recommend this tutorial. You might also want to watch this instructional video.