Professor

Dr. Jesse Deutch

Department of Mathematics

Interests

  1. Computational Number Theory
  2. Quadratic Forms
  3. Quaternion Algebras

Education

1978

Princeton University
USA
Bachelors

1980

NYU
USA
Masters

2012

Brown University
USA
Ph.D.

Experience

  • Multiple years, Chair of Statistics Syllabus Review Committee | University of Botswana, Botswana
  • Multiple years, Member of Pure Maths Syllabus Review Committee | University of Botswana, Botswana
  • 1 year, Member of Faculty of Science Research and Publications Committee | University of Botswana, Botswana
  • 1 year, Departmental Time Table Representative | University of Botswana, Botswana
  • 4 years, Actuarial Science Program lead | University of Northern Colorado, USA
  • 1 year, Actuarial Club Faculty Advisor | University of Northern Colorado, USA
  • 1 year, Chair of Departmental Search Committee | Saginaw Valley State University, USA

Research Interest

  • Use of Geometry of Numbers techniques to demonstrate universality of certain quadratic forms over quadratic fields. Coordinated use of Quaternion Algebras and Geometry of Numbersto resolve universality in some cases.
  • Computational investigations into properties of algebraic integers, algebraic number fields and related structures. Use of computer algebra systems, Python and C in these investigations.

Awards & Fellowships

  • 1985 – PSC-CUNY Research Award Program
  • 1986 - PSC-CUNY Research Award Program

Memberships

  • American Mathematical Society, formerly member of IEEE, formerly student member of Faculty of Actuaries (U.K.).

Publications

  • A Non-Classical Quadratic Form of Hessian Discriminant 4 is Universal over Q(),  Jesse Deutsch, INTEGERS EJCNT 16, #A19 (2016)
  • Conjectures on the Fundamental Domain of the Hilbert Modular Group, Jesse Deutsch, Computers and Math. with Applications, 59, 700-705 (2010)
  • Universality of a Non-Classical Integral Quadratic Form over Q(), Jesse Deutsch,ActaArithmetica, 136.3, 229-242 (2009)
  • Short Proofs of the Universality of Certain Diagonal Quadratic Forms, Jesse Deutsch, Archiv. der Math. 91, 44-48 (2008)
  • A Quaternionic Proof of the Universality of some Quadratic Forms, Jesse Deutsch,INTEGERS EJCNT, 8.2, #A3 (2008)
  • Bumby’s Technique and a Result of Liouville on a Quadratic Form, Jesse Deutsch,INTEGERS ECJNT, 8.2, #A2 (2008)
  • A Quaternionic Proof of the Representation Formula of a Quaternary Quadratic Form, Jesse Deutsch,Jour. of Number Theory, 113, 149-174 (2005)
  • An Alternate Proof of Cohn’s Four Squares Theorem, Jesse Deutsch,Jour. of Number Theory, 104, 263-278 (2004)
  • Geometry of Numbers Proof of Gotzky’s Four Squares Theorem, Jesse Deutsch,Jour. of Number Theory, 96.2, 417-431 (2002)
  • A Computational Approach to Hilbert Modular Group Fixed Points, Jesse Deutsch, Math. Of Computation, 71, 1271-1280 (2002)
  • The Modular Equations of Norm 3 for Q(), Jesse Deutsch, Computers and Math. With Applications, 42 (10-11), 1291-1301 (2001)
  • On Strongly Regular Graphs with , J. Deutsch and P.H. Fisher, Jour. of Combinatorics, 22, 303-306 (2001)
  • Identities Arising from Hecke Transformations of Modular Forms over Q() and Q(), Jesse Deutsch, Jour. of Symbolic Computation, 15, 315-323 (1993)
  • Some Singular Moduli for Q(), H. Cohn and J. Deutsch, Math. of Computation, 59, 213-247 (1992)
  • Conjectures Relating to a Generalization of the Ramanujan Tau Function, Jesse Deutsch, Number Theory – New York Seminar 1989-1990, Springer-Verlag, 105-118 (1991)
  • An Explicit Modular Equation in Two Variables for Q(), H. Cohn and J.I. Deutsch, Math. of Computation, 50, 557-568 (1988)
  • Application of Symbolic Manipulation to the Hecke Transformations of Modular Forms in Two Variables II, H. Cohn and J.I. Deutsch, Jour. of Symbolic Computation, 4, 35-40 (1987)
  • Application of Symbolic Manipulation to Hecke Transformations of Modular Forms in Two Variables, H. Cohn and J.I. Deutsch, Math. of Computation, 48, 139-146 (1987)
  • Use of a Computer Scan to Prove Q and Q are Euclidean, H. Cohn and J. Deutsch, Math. of Computation, 46, 295-299 (1986)

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