Research Interests
- Classical and adelic modular forms
- Local and global representation theory
- Automorphic L-functions
Selected Publications and Preprints
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Dimension formulas for Siegel modular forms of level 4 (with Manami Roy and Shaoyun Yi).
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Mathematika 69 (2023), 795-840. DOI
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pdf
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The special values of the standard L-functions for GSp2n x GL1 (with Shuji Horinaga, Ameya Pitale and Abhishek Saha).
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Trans. Amer. Math. Soc. 375 (2022), 6947-6982. DOI
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pdf
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Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series (with Ameya Pitale and Abhishek Saha).
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Publ. Math 66 (2022), 405-434. DOI
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pdf
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On counting cuspidal automorphic representations for GSp(4) (with Manami Roy and Shaoyun Yi).
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Forum Math. 33 (2021), 821-843. DOI
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pdf
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On the standard L-function for GSp2n x GL1 and algebraicity of symmetric fourth L-values for GL2 (with Ameya Pitale and Abhishek Saha).
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Ann. Math. Québec 45 (2021), 113-159. DOI
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pdf
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Lowest weight modules of Sp4(R) and nearly holomorphic Siegel modular forms (with Ameya Pitale and Abhishek Saha).
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Kyoto J. Math. 61 (2021), 745-814. DOI
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arXiv
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Explicit refinements of Böcherer's conjecture for Siegel modular forms of square-free level (with Martin Dickson, Ameya Pitale and Abhishek Saha).
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J. Math. Soc. Japan 72 (2020), 251-301
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pdf
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Paramodular forms in CAP representations of GSp(4)
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Acta Arith. 194 (2020), 319-340
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pdf
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On Klingen Eisenstein series with level in degree two (with Alok Shukla).
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J. Ramanujan Math Soc. 34 (2019), 373-388
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pdf
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Paramodular forms of level 16 and supercuspidal representations (with Cris Poor and David Yuen).
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Mosc. J. Comb. Number Theory 8 (2019), 289-324
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pdf website
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Analytic L-functions: Definitions, theorems, and connections (with David Farmer, Ameya Pitale and Nathan Ryan).
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Bull. Amer. Math. Soc., 2018 DOI
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pdf
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Zeta integrals for GSp(4) via Bessel models (with Long Tran).
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Pacific J. Math. 296 (2018), 437-480 DOI
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pdf
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Paramodular forms of level 8 and weights 10 and 12 (with Cris Poor and David Yuen).
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Int. J. Number Theory 14 (2018), 417-467 DOI
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pdf
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Triply imprimitive representations of GL(2) (with Salam Turki).
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Proc. Amer. Math. Soc. 146 (2018), 971-981 DOI
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pdf
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Packet structure and paramodular forms.
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Trans. Amer. Math. Soc. 370 (2018), 3085-3112 DOI
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pdf
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Archimedean aspects of Siegel modular forms of degree 2.
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Rocky Mountain J. Math 47 (2017), 2395-2436
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pdf
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A note on the growth of nearly holomorphic vector-valued Siegel modular forms (with Ameya Pitale and Abhishek Saha).
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In L-functions and Automorphic Forms, Contributions in Mathematical and Computational Sciences, Springer, 2017.
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pdf
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Local and global Maass relations (with Ameya Pitale and Abhishek Saha).
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Math. Z. 287 (2017), 655-677
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pdf
expanded version
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Some remarks on Bessel functionals for GSp(4) (with Brooks Roberts).
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Documenta Math. 21 (2016), 467-553
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pdf
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Representations of SL_2(R) and nearly holomorphic modular forms (with Ameya Pitale and Abhishek Saha).
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Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1973 (2015), 141-153
(This note may be viewed as an introduction to the previous paper.)
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arXiv
proceedings
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Transfer of Siegel cusp forms of degree 2 (with Ameya Pitale and Abhishek Saha).
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Mem. Amer. Math. Soc. 232 (2014), no. 1090, vi+107 pp
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pdf
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Bessel models for GSp(4): Siegel vectors of square-free level (with Ameya Pitale).
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J. Number Theory 136 (2014), 134-164
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published version (31 pages)
long version with additional details (89 pages)
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Irreducibility criteria for local and global representations (with Hiro-Aki Narita and Ameya Pitale).
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Proc. Amer. Math. Soc. 141 (2013), 55-63
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pdf
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Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions (with Abhishek Saha).
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J. Lond. Math. Soc. 88 (2013), 251-270
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pdf
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Survey article: Characterizations of the Saito-Kurokawa lifting (with David Farmer, Ameya Pitale and Nathan Ryan).
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Rocky Mountain J. Math. 43 (2013), 1747-1757
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pdf
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Testing the functional equation of a high-degree Euler product (with David Farmer and Nathan Ryan).
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Pacific J. Math 253 (2011), 349-366
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pdf
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On the number of local newforms in a metaplectic representation (with Brooks Roberts).
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In: Arithmetic Geometry and Automorphic Forms, International Press and Higher Education Press, 2011
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pdf
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Ramanujan-type results for Siegel cusp forms of degree 2 (with Ameya Pitale).
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J. Ramanujan Math. Soc. 24 (2009), 87-111
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pdf
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Bessel models for lowest weight representations of GSp(4,R) (with Ameya Pitale).
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Int. Math. Res. Not. 2009, 1159-1212
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pdf
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Integral representation for L-functions for GSp(4) x GL(2) (with Ameya Pitale).
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J. Number Theory 129 (2009), 1272-1324
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pdf
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On the adjoint L-function of the p-adic GSp(4) (with Mahdi Asgari).
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J. Number Theory 128 (2008), 2340-2358
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pdf
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Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2 (with Ameya Pitale).
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Proc. Amer. Math. Soc. 136 (2008), 3831-3838
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pdf
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Local Newforms for GSp(4) (with Brooks Roberts).
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Springer Lecture Note in Mathematics, vol. 1918 (2007)
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pdf
errata
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On classical Saito-Kurokawa liftings.
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J. Reine Angew. Math. 604 (2007), 211-236
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pdf
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On modular forms for the paramodular group (with Brooks Roberts).
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In: Automorphic Forms and Zeta Functions. Proceedings of the Conference in Memory of Tsuneo Arakawa. World Scientific, 2006
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pdf
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An alternative proof of a theorem on local newforms for GSp(4) (with Brooks Roberts).
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Proceedings of the 9th Autumn Workshop on Number Theory, Hakuba, Japan, 2006
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pdf
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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).
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Proceedings of the 9th Autumn Workshop on Number Theory, Hakuba, Japan, 2006
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pdf
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Iwahori-spherical representations of GSp(2) and Siegel modular forms of degree 2 with square-free level.
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J. Math. Soc. Japan 57 (2005), 259-293
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pdf
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The Saito-Kurokawa lifting and functoriality.
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Amer. J. Math. 127 (2005), 209-240
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pdf
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New vectors for GSp(4): a conjecture and some evidence (with Brooks Roberts).
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Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 107-121
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pdf
proceedings
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On the spin L-function of Ikeda's lifts.
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Comment. Math. Univ. St. Paul 52 (2003), 1-46
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pdf
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On Siegel modular forms of degree 2 with square-free level.
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Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 155-169
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pdf
proceedings
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On the archimedean Euler factors for spin L-functions.
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Abh. Math. Sem. Univ. Hamburg 72 (2002), 119-143
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pdf
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Some remarks on local newforms for GL(2).
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J. Ramanujan Math. Soc. 17 (2002), 115-147
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pdf
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Siegel modular forms and representations (with Mahdi Asgari).
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Manuscripta Math. 104 (2001), 173-200
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pdf
Tables for Representations of GSp(4)
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Tables for Representations of GSp(4) (with Brooks Roberts).
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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.
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pdf
latex
TORA
Texas-Oklahoma Representations and Automorphic Forms is a regional conference series organized jointly by
UNT,
OSU and
OU. The TORA meetings so far:
- TORA I, September 17-18, 2011, at UNT
- TORA II, April 6-8, 2012, at OSU
- TORA III, September 28-30, 2012, at OU
- TORA IV, March 23-24, 2013, at UNT
- TORA V, September 20-22, 2013, at OSU
- TORA VI, March 7-9, 2014, at OU
- TORA-S I (student TORA), March 28-29, 2015, at OU
- TORA VII, April 8-10, 2016, at UNT
- TORA VIII, March 31 - April 2, 2017, at OSU
- TORA IX, April 7-8, 2018, at OU
- TORA X, April 5-7, 2019, at UNT
- TORA XI, April 1-3, 2022, at OSU
TORA is made possible by grants from the NSF and support from the three Universities.
Other Material