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

Course Information for Students


TORA

Texas-Oklahoma 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 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 is made possible by grants from the NSF. The OU meetings were supported by NSF grants DMS-1132510 and DMS-1302751. 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), 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
  • pdf
  • Local Newforms for GSp(4).
  • Springer Lecture Note in Mathematics, vol. 1918 (2007)
  • pdf     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
  • pdf
  • 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
  • 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
  • Some remarks on Bessel functionals for GSp(4).
  • Documenta Math. 21 (2016), 467-553
  • pdf

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

Saito-Kurokawa and Ikeda Lifting

  • On the spin L-function of Ikeda's lifts.
  • Comment. Math. Univ. St. Paul 52 (2003), 1-46
  • pdf
  • The Saito-Kurokawa lifting and functoriality.
  • Amer. J. Math. 127 (2005), 209-240
  • pdf
  • On classical Saito-Kurokawa liftings.
  • J. Reine Angew. Math. 604 (2007), 211-236
  • pdf
  • Joint with David Farmer, Ameya Pitale and Nathan Ryan: Survey article: Characterizations of the Saito-Kurokawa lifting.
  • Rocky Mountain J. Math. 43 (2013), 1747-1757
  • pdf
  • Joint with Ameya Pitale and Abhishek Saha: Local and global Maass relations.
  • Preprint, 2013
  • pdf     expanded version

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
  • pdf
  • Joint with Ameya Pitale: Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2.
  • Proc. Amer. Math. Soc. 136 (2008), 3831-3838
  • pdf
  • Joint with Ameya Pitale: Ramanujan-type results for Siegel cusp forms of degree 2.
  • J. Ramanujan Math. Soc. 24 (2009), 87-111
  • pdf
  • A remark on a paper of Ibukiyama and Skoruppa.
  • Abh. Math. Sem. Univ. Hamburg 79 (2009), 189-191
  • pdf
  • Joint with David Farmer and Nathan Ryan: Testing the functional equation of a high-degree Euler product.
  • Pacific J. Math 253 (2011), 349-366
  • pdf
  • Joint with Abhishek Saha: Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions.
  • J. Lond. Math. Soc. 88 (2013), 251–270
  • pdf
  • 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
  • pdf
  • Packet structure and paramodular forms.
  • Preprint, 2016
  • pdf

Other

  • Joint with Mahdi Asgari: Siegel modular forms and representations.
  • Manuscripta Math. 104 (2001), 173-200
  • pdf
  • Some remarks on local newforms for GL(2).
  • J. Ramanujan Math. Soc. 17 (2002), 115-147
  • pdf
  • On the archimedean Euler factors for spin L-functions.
  • Abh. Math. Sem. Univ. Hamburg 72 (2002), 119-143
  • pdf
  • Joint with Mahdi Asgari: On the adjoint L-function of the p-adic GSp(4).
  • J. Number Theory 128 (2008), 2340-2358
  • pdf
  • Joint with Hiro-Aki Narita and Ameya Pitale: Irreducibility criteria for local and global representations.
  • Proc. Amer. Math. Soc. 141 (2013), 55–63
  • pdf

Other Material

  • The Sato-Tate Pages. An easy introduction to the Sato-Tate 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.