Joshua Friedman PhD





Analytical number theory: Selberg trace formulas, Selberg zeta-functions, modular forms, Hecke operators, computational number theory; Fuchsian and Kleinian groups, arithmetic groups; Data Mining


  1. PhD thesis: The Selberg trace formula and Selberg zeta-function for confinite Kleinian Groups with finite-dimensional unitary representations. (math.NT/0612807)
  2. The Selberg trace formula and Selberg zeta-function for confinite Kleinian Groups with finite-dimensional unitary representations. Math. Z. Volume 250, Number 4 / August, 2005 (SpringerLink - Journal Article) [math/0410067]
  3. The regularized determinant of the Laplace operator for confinite Kleinian Groups with finite-dimensional unitary representations.  Communications in Mathematical Physics Volume 275, Number 3 / November, 2007 (math.NT/0605288)
  4. Analogues of the Artin factorization formula for the automorphic scattering matrix and Selberg zeta-function associated to a Kleinian group. (Proceedings of the American Mathematical Society). (math.NT/0702030)
  5. The Selberg trace formula for Hecke operators on cocompact Kleinian groups (arXiv:0710.5787)
  6. An effective bound for the Huber constant for cofinite Fuchsian groups, with Jay Jorgenson and Jurg Kramer (arXiv:1003.1652) Published in Mathematics of Computation
  7. Uniform sup-norm bounds on average for cusp forms of higher weights, with Jay Jorgenson and Jurg Kramer (arXiv:1305.1348) To be submitted.

Current Math Courses

Calculus One and Two: Single variable calculus, differentiation, integration, infinite series.

Differential Equations: Ordinary diffEQs, Fourier series, Boundary value problems.

Probability and Statistics: Calculus and non-calculus based approaches.

Quantitative Methods: Operations research, linear programming, transportation problems, network problems.

Data Mining and Java Programming (currently in preparation).


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