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

Research Interests

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

Course Information for Students


Selected Publications and Preprints

  • Paramodular forms in CAP representations of GSp(4)
  • Preprint, 2018
  • pdf
  • Analytic L-functions: Definitions, theorems, and connections (with David Farmer, Ameya Pitale and Nathan Ryan).
  • Preprint, 2018
  • pdf
  • Paramodular forms of level 16 and supercuspidal representations (with Cris Poor and David Yuen).
  • Preprint, 2018
  • pdf    website
  • Zeta integrals for GSp(4) via Bessel models (with Long Tran).
  • Pacific J. Math. 296 (2018), 437–480 DOI
  • pdf
  • Paramodular forms of level 8 and weights 10 and 12 (with Cris Poor and David Yuen).
  • Int. J. Number Theory 14 (2018), 417-467 DOI
  • pdf
  • Triply imprimitive representations of GL(2) (with Salam Turki).
  • Proc. Amer. Math. Soc. 146 (2018), 971-981 DOI
  • pdf
  • Packet structure and paramodular forms.
  • Trans. Amer. Math. Soc. 370 (2018), 3085-3112 DOI
  • pdf
  • Archimedean aspects of Siegel modular forms of degree 2.
  • Rocky Mountain J. Math 47 (2017), 2395-2436
  • pdf
  • A note on the growth of nearly holomorphic vector-valued Siegel modular forms (with Ameya Pitale and Abhishek Saha).
  • In L-functions and Automorphic Forms, Contributions in Mathematical and Computational Sciences, Springer, 2017.
  • pdf
  • Local and global Maass relations (with Ameya Pitale and Abhishek Saha).
  • Math. Z. 287 (2017), 655–677
  • pdf     expanded version
  • Some remarks on Bessel functionals for GSp(4) (with Brooks Roberts).
  • Documenta Math. 21 (2016), 467-553
  • pdf
  • 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), 141-153
    (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
  • pdf
  • Bessel models for GSp(4): Siegel vectors of square-free level (with Ameya Pitale).
  • J. Number Theory 136 (2014), 134-164
  • published version (31 pages)      long version with additional details (89 pages)
  • Irreducibility criteria for local and global representations (with Hiro-Aki Narita and Ameya Pitale).
  • Proc. Amer. Math. Soc. 141 (2013), 55–63
  • pdf
  • Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions (with Abhishek Saha).
  • J. Lond. Math. Soc. 88 (2013), 251–270
  • pdf
  • Survey article: Characterizations of the Saito-Kurokawa lifting (with David Farmer, Ameya Pitale and Nathan Ryan).
  • Rocky Mountain J. Math. 43 (2013), 1747-1757
  • pdf
  • Testing the functional equation of a high-degree Euler product (with David Farmer and Nathan Ryan).
  • Pacific J. Math 253 (2011), 349-366
  • 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
  • pdf
  • Ramanujan-type results for Siegel cusp forms of degree 2 (with Ameya Pitale).
  • J. Ramanujan Math. Soc. 24 (2009), 87-111
  • pdf
  • Bessel models for lowest weight representations of GSp(4,R) (with Ameya Pitale).
  • Int. Math. Res. Not. 2009, 1159-1212
  • pdf
  • Integral representation for L-functions for GSp(4) x GL(2) (with Ameya Pitale).
  • J. Number Theory 129 (2009), 1272-1324
  • pdf
  • On the adjoint L-function of the p-adic GSp(4) (with Mahdi Asgari).
  • J. Number Theory 128 (2008), 2340-2358
  • pdf
  • Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2 (with Ameya Pitale).
  • Proc. Amer. Math. Soc. 136 (2008), 3831-3838
  • pdf
  • Local Newforms for GSp(4) (with Brooks Roberts).
  • Springer Lecture Note in Mathematics, vol. 1918 (2007)
  • pdf     errata
  • On classical Saito-Kurokawa liftings.
  • J. Reine Angew. Math. 604 (2007), 211-236
  • pdf
  • 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
  • pdf
  • 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
  • pdf
  • 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
  • pdf
  • 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
  • pdf
  • The Saito-Kurokawa lifting and functoriality.
  • Amer. J. Math. 127 (2005), 209-240
  • pdf
  • New vectors for GSp(4): a conjecture and some evidence (with Brooks Roberts).
  • Surikaisekikenkyusho Kokyuroku (Research Institute for Mathematical Sciences, Kyoto University) 1338 (2003), 107-121
  • pdf     proceedings
  • On the spin L-function of Ikeda's lifts.
  • Comment. Math. Univ. St. Paul 52 (2003), 1-46
  • pdf
  • 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
  • On the archimedean Euler factors for spin L-functions.
  • Abh. Math. Sem. Univ. Hamburg 72 (2002), 119-143
  • pdf
  • Some remarks on local newforms for GL(2).
  • J. Ramanujan Math. Soc. 17 (2002), 115-147
  • pdf
  • Siegel modular forms and representations (with Mahdi Asgari).
  • Manuscripta Math. 104 (2001), 173-200
  • pdf

Tables for Representations of GSp(4)

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

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 is made possible by grants from the NSF. The OU meetings were supported by NSF grants DMS-1132510, DMS-1302751 and DMS-1601105. The predecessor to the TORA conference series was this event.

Other Material

  • The Sato-Tate Pages. An easy introduction to the Sato-Tate conjecture, created in collaboration with Julian Rosen. Contains some historical remarks.
  • Arthur packets for GSp(4). A table summarizing the six types of Arthur packets contributing to the discrete automorphic spectrum of GSp(4).
  • The top 10 signs that you are not a real mathematician.