Joshua Friedman PhD

Research

Disclaimers

crowneagle@gmail.com

Research

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

Mathematics Papers

  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 Volume 136, Number 10, October 2008). (Journal Link) (math.NT/0702030)
  5. An effective bound for the Huber constant for cofinite Fuchsian groups, with Jay Jorgenson and Jurg Kramer (Journal Link) (arXiv:1003.1652) Published in Math. Comp. 80 (2011), 1163-1196
  6. Uniform sup-norm bounds on average for cusp forms of higher weights, with Jay Jorgenson and Jurg Kramer Journal Link (arXiv:1305.1348) Published in ( Ballmann W., Blohmann C., Faltings G., Teichner P., Zagier D. (eds) Arbeitstagung Bonn 2013. Progress in Mathematics, vol 319. Birkhauser, Cham)
  7. On the minimal distance between elliptic fixed points for geometrically finite Fuchsian groups (2016) Journal Link (arXiv:1406.5028) Published in International Journal of Number Theory 12 (06), 1663-1668
  8. Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps (2018) Accepted at Contemporary Mathematics (AMS) with Jay Jorgenson, Lejla Smajlovic (arXiv:1701.06869)
  9. The determinant of the Lax-Phillips scattering operator with Jay Jorgenson, Lejla Smajlovic (submitted ) (arXiv:1603.07613)
  10. Effective sup-norm bounds on average for cusp forms of even weight with Jay Jorgenson and Jurg Kramer (submitted ) (arXiv:1801.05740)

Artificial Intelligence and Operations Research Papers

  1. Automated timetabling for small colleges and high schools using huge integer programs (Submitted) (arXiv:1612.08777)

Unpublished Preprints

  1. The Selberg trace formula for Hecke operators on cocompact Kleinian groups (arXiv:0710.5787)
  2. An evaluation of the central value of the automorphic scattering determinant with Jay Jorgenson and Lejla Smajlovic (arXiv:1607.08053)

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.

Operations research, linear programming, transportation problems, network problems, stochastic models, queuing theory

An Introduction to Python and Artificial Intelligence: Neural networks

Disclaimer

This website is a personal endeavor of Joshua S. Friedman. Though I am an employee of the United States Government, (US Merchant Marine Academy, Kings Point) this webpage does not reflect their will or views in any way. This webpage does not reflect the will of views of the US Department of Transportation, the Maritime Administration, or the US Merchant Marine Academy.