Thomas R. Shemanske

Dartmouth College (603) 646-3179 (office)
Department of Mathematics (603) 646-1312 (fax)
Hanover, NH 03755-3551 thomas.r.shemanske@dartmouth.edu

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


  • A. W. Mellon Foundation: “A Better Calculus for Less” (Dwight Lahr, PI), ($224K approx) July 1, 2000 - June 30, 2003. [1 month of support, Summer 2003]
  • AT&T Foundation: (co-PI, funded) “Development and Dissemination of a Free, Online Calculus Course for College and High School Students” (DC 5-38132), $50k, July 1, 2003 - June 30, 2006.
  • Hewlett Foundation: (co-PI, proposed) “Opening Access to Quality Calculus”, $400k, July 1, 2003 - June 30, 2006.
  • A. W. Mellon Foundation: “A Better Calculus for Less” (Dwight Lahr, PI), ($224K approx) July 1, 2000 - June 30, 2003. [1 month of support, Summer 2000]
  • NSF Grant USE 8953908:(Co-Principal Investigator 1990-1991) “Calculus: Restructuring and Integration with Computing” (3-year grant to carry out calculus reform), ($300K approx) 1989 - 1992.
  • Sloan Foundation Grant 89-10-1: “Computers and the teaching of Mathematics”, ($80K approx) November, 1989 - November 1990.
  • NSF Grant USE 8814009: “Calculus: Restructuring and Integration with Computing” (planning grant for revision of calculus curriculum), ($50K approx) 1988 - 1989.
   2021– Professor Emeritus Dartmouth College
   2004–2007 Department Chair Dartmouth College
   1994 (Fall) Member MSRI
   1993–2021 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 $GL_n(K)$ and $Sp_n(K)$, $K$ 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
Angelica Babei McMaster University 2019 On the Arithmetic of Tiled Orders
Michael Wijaya Bard HS Early College Queens 2015 A function-field analogue of Conway's Topograph
Benjamin Linowitz Oberlin College 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 University 2005 Calculating Satake parameters
Susan D'Agostino Editor/Writer/Mathematician 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 Former Head:Investment Strategy/Portfolio Mgr, Parametric Portfolio Assoc 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
  • National Science Foundation
  • National Security Agency
  • Mathematical Reviews
  • Zentralblatt für Mathematik

  • Acta Arithmetica
  • Glasgow Mathematical Journal
  • International Journal of Number Theory
  • Journal of Number Theory
  • London Math Society
  • Pacific Journal of Mathematics
  • Ramanujan Journal
  • Rocky Mountain Journal
  • Transactions of the American Mathematical Society
  • American Mathematical Society
  • Mathematical Association of America
[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. Modern Cryptography and Elliptic Curves: A Beginner's Guide, STML 83, AMS, 252 pages, 2017, ISBN: 978-1-4704-3582-0.
[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 $GL_n$ and Buildings, Acta Arithmetica 112, (2004), 131 - 140.
  18. The Arithmetic and Combinatorics of Buildings for $Sp_n$ 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, International Journal of Number Theory. 13, No. 4, pp. 853--884 (2017)
  25. (with J. Jorgenson, L. Smajlovic) Lynne Heather Walling, a memorial article, submitted to the Notices of the AMS.
[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