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

Course Information for Students
Selected Publications and Preprints

Paramodular forms in CAP representations of GSp(4)

Preprint, 2018

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Analytic Lfunctions: Definitions, theorems, and connections (with David Farmer, Ameya Pitale and Nathan Ryan).

Bull. Amer. Math. Soc., 2018 DOI

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Paramodular forms of level 16 and supercuspidal representations (with Cris Poor and David Yuen).

Preprint, 2018

pdf website

On the standard Lfunction for GSp_{2n} x GL_{1} and algebraicity of symmetric fourth Lvalues for GL_{2} (with Ameya Pitale and Abhishek Saha).

Preprint, 2017

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Zeta integrals for GSp(4) via Bessel models (with Long Tran).

Pacific J. Math. 296 (2018), 437–480 DOI

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Paramodular forms of level 8 and weights 10 and 12 (with Cris Poor and David Yuen).

Int. J. Number Theory 14 (2018), 417467 DOI

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Triply imprimitive representations of GL(2) (with Salam Turki).

Proc. Amer. Math. Soc. 146 (2018), 971981 DOI

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Packet structure and paramodular forms.

Trans. Amer. Math. Soc. 370 (2018), 30853112 DOI

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Archimedean aspects of Siegel modular forms of degree 2.

Rocky Mountain J. Math 47 (2017), 23952436

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A note on the growth of nearly holomorphic vectorvalued Siegel modular forms (with Ameya Pitale and Abhishek Saha).

In Lfunctions and Automorphic Forms, Contributions in Mathematical and Computational Sciences, Springer, 2017.

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Local and global Maass relations (with Ameya Pitale and Abhishek Saha).

Math. Z. 287 (2017), 655–677

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expanded version

Some remarks on Bessel functionals for GSp(4) (with Brooks Roberts).

Documenta Math. 21 (2016), 467553

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

Preprint, 2015

arXiv

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

Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1973 (2015), 141153
(This note may be viewed as an introduction to the previous paper.)

arXiv
proceedings

Transfer of Siegel cusp forms of degree 2 (with Ameya Pitale and Abhishek Saha).

Mem. Amer. Math. Soc. 232 (2014), no. 1090, vi+107 pp

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Bessel models for GSp(4): Siegel vectors of squarefree level (with Ameya Pitale).

J. Number Theory 136 (2014), 134164

published version (31 pages)
long version with additional details (89 pages)

Irreducibility criteria for local and global representations (with HiroAki Narita and Ameya Pitale).

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

pdf

Yoshida lifts and simultaneous nonvanishing of dihedral twists of modular Lfunctions (with Abhishek Saha).

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

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

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

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

Pacific J. Math 253 (2011), 349366

pdf

On the number of local newforms in a metaplectic representation (with Brooks Roberts).

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

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Ramanujantype results for Siegel cusp forms of degree 2 (with Ameya Pitale).

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

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Bessel models for lowest weight representations of GSp(4,R) (with Ameya Pitale).

Int. Math. Res. Not. 2009, 11591212

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Integral representation for Lfunctions for GSp(4) x GL(2) (with Ameya Pitale).

J. Number Theory 129 (2009), 12721324

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

J. Number Theory 128 (2008), 23402358

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Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2 (with Ameya Pitale).

Proc. Amer. Math. Soc. 136 (2008), 38313838

pdf

Local Newforms for GSp(4) (with Brooks Roberts).

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

pdf
errata

On classical SaitoKurokawa liftings.

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

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On modular forms for the paramodular group (with Brooks Roberts).

In: Automorphic Forms and Zeta Functions. Proceedings of the Conference in Memory of Tsuneo Arakawa. World Scientific, 2006

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

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 (with Brooks Roberts).

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

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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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The SaitoKurokawa lifting and functoriality.

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

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New vectors for GSp(4): a conjecture and some evidence (with Brooks Roberts).

Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 107121

pdf
proceedings

On the spin Lfunction of Ikeda's lifts.

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

pdf

On Siegel modular forms of degree 2 with squarefree level.

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

pdf
proceedings

On the archimedean Euler factors for spin Lfunctions.

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

pdf

Some remarks on local newforms for GL(2).

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

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Siegel modular forms and representations (with Mahdi Asgari).

Manuscripta Math. 104 (2001), 173200

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Tables for Representations of GSp(4)

Tables for Representations of GSp(4) (with Brooks Roberts).

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
TORA
TexasOklahoma Representations and Automorphic Forms is a regional conference series organized jointly by
UNT,
OSU and
OU. The TORA meetings so far:
 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 VII, April 810, 2016, at UNT
 TORA VIII, March 31  April 2, 2017, at OSU
 TORA IX, April 78, 2018, at OU
TORA is made possible by grants from the NSF. The OU meetings were supported by NSF grants
DMS1132510,
DMS1302751 and
DMS1601105.
The predecessor to the TORA conference series was
this event.
Other Material