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Thomas R. Shemanske

Dartmouth College        (603) 646-3179 (office)
Department of Mathematics   (603) 646-1312 (fax)
Hanover, NH 03755-3551


Ph.D.    University of Rochester    1979
M.A.    University of Rochester    1976
A.B.    Cornell University    1974



   2004--2007    Department Chair    ---    Dartmouth College
   1994   Fall    Member    ---    MSRI
   1993--present    Professor    ---    Dartmouth College
   1987--1993    Associate Professor    ---    Dartmouth College
   1981--1987    Assistant Professor    ---    Dartmouth College
   1979--1981    Lawton Lecturer    ---    Temple University


My research is in algebraic number theory with a particular interest in the theory of modular forms, central simple algebras, and the theory of buildings and their applications. I have done extensive work on questions of the representability of modular forms by theta series attached to quadratic forms, and have used the arithmetic of quaternion algebras to answer questions regarding the representation numbers of ternary and quaternary quadratic forms. Other work has included aspects of the theory of newforms for integral and half-integral weight modular forms of elliptic and Hilbert type as well as the study of higher rank Hecke operators and their relation to Bruhat-Tits buildings for GLn(K) and Spn(K), K a local field. Recent work has focused on the geometric and combinatorial aspects of affine buildings, as well as their application to the study of arithmetic in central simple algebras.


Student Name Current Affiliation Degree Year Thesis title
Michael Wijaya Dartmouth College 2015 A function-field analogue of Conway's Topograph
Benjamin Linowitz U of Michigan 2012 Selectivity in Central Simple Algebras and Isospectrality
Alison Setyadi Department of Defense 2007 The Affine Buildings of SL_n and Sp_n: A Combinatorial Perspective
Nathan Ryan Bucknell 2005 Calculating Satake parameters
Susan D'Agostino Southern NH Univ 2003 Classifying Additive Codes
Holly Rosson Warren Wilson College 2000 Theta functions over function fields
Sharon Frechette Holy Cross 1997 Decomposition of Spaces of Half-Integral Weight Cusp Forms
Tamara Veenstra University of Redlands 1997 Characterizing Siegel Modular Forms
Timothy Atwill Parametric 1993 Diagonalizing Spaces of Hilbert Cusp Forms
Lynne Walling University of Bristol, UK 1987 Theta Series attached to Lattices of Arbitrary Rank


John Wesley Young Research Instructors at Dartmouth
   Name    Current Affiliation    Years
   Cristina Ballantine    Holy Cross    2000--2002
   Anne Schwartz    U Mass, Amherst    1989--1991
   Jacob Nemchenok    Private Industry    1985-1987
   John Cremona    Warwick Mathematics Institute, UK    1982--1984




Books and Monographs

  1. (with H. Hijikata and A. Pizer), The Basis Problem for Modular Forms on Gamma_0(N) Memoirs of the AMS, 418 (1989), 159 pages.

  2. (underr development) Working title: From Calculus to Applications of Elliptic Curves, 138 pages.

Research Articles

  1. (with H. Hijikata and A. Pizer), The Basis Problem for Modular Forms on Gamma_0(N), Proc. Japan Acad., 56 (1980), pp. 280-284.

  2. Cuspidal Newforms and Character Twists, J. reine angew. Math., 328 (1981), pp. 58-71.

  3. Primitive Newforms of Weight 3/2, Acta Arith., 43 (1984), pp. 97-104.

  4. Ternary Quadratic Forms and the Arithmetic of Quaternion Algebras, preprint.

  5. Representations of Ternary Quadratic Forms and the Class Number of Imaginary Quadratic Fields, Pacific J. of Math., 122 (1986), pp. 223-250.

  6. Ternary Quadratic Forms and Quaternion Algebras, Journal of Number Theory 23 (1986), pp. 203-209.

  7. (with H. Hijikata and A. Pizer), Orders in Quaternion Algebras, J. reine angew. Math. 394 (1989), pp. 59-106.

  8. (with H. Hijikata and A. Pizer), Twists of Newforms, Journal of Number Theory 35 (1990), pp 287 - 324.

  9. (with L. Walling) On the Shimura Lift for Hilbert Modular Forms, in A Tribute to Emil Grosswald: Number Theory and Related Analysis, Contemporary Mathematics, Volume 143, Knopp and Sheingorn Editors, American Mathematical Society, March 1993, pp 561 - 569.

  10. (with L. Walling), Twists of Hilbert Modular Forms, Transactions of the AMS, 338, (1993), 375 - 403.

  11. (with L. Walling), Determining Multiplicities of Half-Integral Weight Newforms, Pacific Journal of Math., 167, (1995), 345 - 383.

  12. (with L. Walling), A Characterization of Simultaneous Hecke Eigenforms, preprint

  13. (with A. Schwartz), Maximal Orders in Central Simple Algebras and Bruhat-Tits Buildings, Journal of Number Theory, 56, (1996), 115 - 138.

  14. Newforms of Half-Integral Weight, Nagoya Math J. 143, (1996), 147 - 169.

  15. (with C. Ballantine) Rolle's Theorem over Local Fields (preprint)

  16. (with J. Rhodes), Rationality Theorems for Hecke Operators on GLn, J. of Number Theory 102, (2003), 278 - 297.

  17. (with C. Ballantine and J. Rhodes), Hecke Operators for GLn and Buildings, Acta Arithmetica 112, (2004), 131 - 140.

  18. The Arithmetic and Combinatorics of Buildings for Spn Transactions AMS 359, (2007), 3409-3423.

  19. Hecke Operators, Zeta Functions, and the Satake Map (preprint)

  20. (with N. Ryan) Inverting the Satake Map for $Sp_n$ and applications to Hecke Operators, Ramanujan J. 17 (2), 2008, 219 -- 244.

  21. (with S. Treneer, L. Walling) Constructing Simultaneous Hecke Eigenforms, International J. Number Theory 6 (5), 2010, 1117 -- 1137.

  22. Split Orders and Convex Polytopes in Buildings, J. Number Theory, 30 (1), 2010, 101 -- 115.

  23. (with B. Linowitz) Embedding Orders in Central Simple Algebras, Journal de théorie des nombres de Bordeaux, 24 no. 2 (2012), 405 -- 424.

  24. (with B. Linowitz) Local Selectivity of Orders in Central Simple Algebras, arXiv, to appear, International Journal of Number Theory.

Other Published Articles

  1. (with J. Baumgartner, et al.) Teaching Calculus with True BASIC, in Priming the Calculus Pump: Innovations and Resources, MAA Notes 17 (1990), pp 33 - 50.

Other Manuscripts

  1. The Basis Problem for Modular Forms on Gamma_0(2^{2r}M), Ph.D. dissertation, University of Rochester (1979).

  2. Notes on the Shimura-Shintani Correspondence, preprint.

  3. WeBWorK Newbie Guide(versions 1.4, 1.5),(2000), 41 pages

  4. WeBWorK Newbie Guide -- version 1.7, (2002), 68 pages

  5. WeBWorK Installation and Course Setup Guide (local notes version 1.6), (2001), 11 pages

  6. WeBWorK Installation and Course Setup Guide (local notes version 1.7), (2002), 13 pages

  7. WeBWorK Installation and Course Setup Guide (local notes version 1.8), (2003), 15 pages

  8. Introduction to Mathematics Beyond Calculus

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Last modified on April 10, 2016