Areas of Expertise/Research
- Analytic Number Theory
- Trace Formulas
1985 University of Minnesota - B.S in Mathematics
1985 University of Minnesota - B.S in Statistics
1987 Stanford University - M.S. in Mathematics
1989 Stanford University - Ph.D. in Mathematics
My academic research focuses on analytic aspects of trace formulas, modular forms and number theory. In the process, I frequently employ methods from other areas of mathematics such as partial differential equations, spectral theory and differential geometry. Additionally, I am interested in applications of mathematics to various disciplines, including the social sciences. I have assisted with statistical analysis for questions stemming from the life sciences and finance. I have provided opinions on statistical issues in legal cases, and I have given testimony as an Expert Witness.
Recent publications (past five years)
1. (with J. Cogdell and L. Smajlovi\'c) Evaluating the Mahler measure of linear forms via the Kronecker limit formula on complex projective space. To appear in Trans. Amer. Math. Soc. (29 pages).
2. (with J. Friedman and L. Smajlovi\'c) Super-zeta functions and regularized determinants associated to cofinite Fuchsian groups with finite-dimensional unitary representations. Letters in Mathematical Physics 111 (2021) Article 15.
3. (with L. Smajlovi\'c and H. Then) An approach for computing generators of class fields of imaginary quadratic number fields using the Schwarzian derivative. To appear in Mathematics of Computation (35 pages)
4. (with C. O'Sullivan and L. Smajlovi\'c) Modular Dedekind symbols associated to Fuchsian groups and higher-order Eisenstein series. Research in Number Theory 6 (2020) Paper No. 22, 42 pp.
5. (with C. Burrin, C. O'Sullivan and L. Smajlovi\'c) Transformation laws for generalized Dedekind sums associated to Fuchsian groups. Acta Arithmetica 196 (2020) 139--162.
6. (with J. Friedman and L. Smajlovi\'c) The determinant of the Lax-Phillips scattering operator. Annales de l'Institut Fourier 70 (2020) 915--947.
7. (with J. Cogdell and L. Smajlovi\'c) Spectral construction of non-holomorphic Eisenstein-type series and their Kronecker limit formula. In: Integrability systems and algebraic geometry: A recognition of Emma Previato's work in algebra and geometry, Eds. R. Donagi, T. Shaska, Cambridge University Press, LMS Lecture Notes Series 459 393--427 (2020).
8. (with D. Garbin) Heat kernel asymptotics on sequences of elliptically degenerating Riemann surfaces. Kodai Math. Journal 43 (2020) 84--128.
9. (with L. Smajlovi\'c and H. Then) On the evaluation of singular invariants for canonical generators of certain genus one arithmetic groups. Experimental Math. 29 (2020), 1--27.
10. (with J. Friedman and J. Kramer) Uniform and effective sup-norm bounds for higher weight automorphic forms. Trans. Amer. Math. Soc. 372 (2019), 7735–-7766.
11. (with L. Smajlovi\'c and H. Then) The Hauptmodul at elliptic points of certain arithmetic groups. Journal of Number Theory 204 (2019) 661--682.
12. (with S. Anni, L. Smajlovi\'c and L Walling) Automorphic Forms and Related Topics, Contemporary Mathematics in AMS 732 (2019) viii+286 pages.
13. (with J. Friedman and L. Smajlovi\'c) Superzeta functions and hyperbolic manifolds. In: Automorphic Forms and Related Topics, ed. S. Anni, J. Jorgenson, L. Smajlovi\'c and L. Walling, AMS Contemp. Math. 732 (2019) 57--74.
14. (with L. Smajlovi\'c) Some results in study of Kronecker limit formula and Dedekind sums. In: Automorphic Forms and Related Topics, ed. S. Anni, J. Jorgenson, L. Smajlovi\'c and L. Walling, AMS Contemp. Math. 732 (2019), 101--124.
15. (with A. von Pippich and L. Smajlovi\'c) Applications of Kronecker's limit formula for elliptic Eisenstein series. Annales math\'ematiques du Qu\'ebec 43 (2019) 99--124.
16. (with D. Garbin) Spectral asymptotics on sequences of elliptically degenerating Riemann surfaces. L'Enseignement Math\'ematique 64 (2018) 161--206.
17. (with L. Smajlovi\'c) Distribution results for zeros of the derivative of Selberg's zeta function associated to finite volume Riemann surfaces. Nagoya Math. Journal 228 (2017) 21--71.
18. (with L. Smajlovi\'c and H. Then) Certain aspects of holomorphic function theory on some genus zero arithmetic groups. LMS J. Comput. Math. 19 (2016) 360–-381.
19. (with J. Friedman and J. Kramer) Uniform sup-norm bounds on average for holomorphic automorphic forms. In Arbeitstagung Bonn 2013: In Memory of Friedrich Hirzebruch, eds: W. Ballman, C. Blohmann, G. Faltings, P. Teichner, and D. Zagier, Progress in Mathematics 319, 131--158, Birkhauser, New York, 2016.
20. (with A. von Pippich and L. Smajlovi\'c) On the wave representation of hyperbolic, elliptic, and parabolic Eisenstein series. Advances in Math. 288 (2016), 887--921.
21. (with L. Smajlovi\'c and H. Then) Kronecker's limit formula, holomorphic modular functions and q-expansions on certain moonshine groups. Experimental Math. 25 (2016), 295--320.
Selected past mathematics publications
1. (edited with D. Goldfeld, P. Jones, D. Ramakirshnan, K. Ribet, and J. Tate) Number theory, Geometry and Analysis: Articles in memory of Serge Lang. 623 pages, Springer, New York, 2012.
2. (with G. Chinta and A. Karlsson) Zeta functions, heat kernels and spectral asymptotics on degenerating families of discrete tori. Nagoya Math. J. 198 (2010) 121-172.
3. (with J. Kramer) Bounds on Faltings's delta function through covers, Annals of Math. 170 (2009) 1-42.
4. (with S. Krantz and contributors) The mathematical contributions of Serge Lang. Notices AMS 54 April 2007, 476-497.
5. (with S. Lang) Spherical Inversion on SL_n(R). Springer-Verlag Monographs in Mathematics, xx+426 pages (2001).
6. (with J. Huntley and R. Lundelius) On the asymptotic behavior of counting functions associated to degenerating hyperbolic Riemann surfaces. J. Func. Analysis 149 (1997) 58-82.
7. (with R. Lundelius) Continuity of relative hyperbolic spectral theory through metric degeneration. Duke Math. J. 84 (1996) 47-81.
8. (with S. Lang) Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series. Math. Ann. 306 (1996) 75-124.
9. On the directional derivatives of the theta function along its divisor. Israel J. of Math. 77 (1992),273-284.
10. Asymptotic behavior of Faltings's delta function. Duke Math. J. 61 (1990), 221-254.
CCNY Teaching Awards
1. (2019) Nominated for CCNY Office of Information Techology Distinguished Ally Award
2. (2015) CCNY Provost's Prize for Pedagogical and Curricular Innovation
3. (2003) The City College of New York Outstanding Mentoring Award
4. (2002) The City College of New York Outstanding Mentoring Award
5. (2002) The City College of New York Outstanding Teaching Award
Selected other publications
1. Espinosa, A., Tikhonov, A. & Jorgenson, J. (2016). Increasing retention in mathematics courses: The role of self-confidence in mathematics on academic performance. Proceedings of the 21st International Academic Conference of the International Institute of Social and Economic Sciences (February), pp. 50-62 (March 13, 2016). doi: 10.20472/IAC.2016.021.012
2. Zheng Zhang, Jun Li, C. N. Manikopoulos, Jay Jorgenson, Jose Ucles, ``Neural Networks in Statistical Anomaly Intrusion Detection," Advances in Scientific Computing, Computational Intelligence and Applications," N. Mastorakis, V. Madlenov, B. Suter and L. J. Wang (Eds.), World Scientific and Engineering Society Press, ISBN: 960-8052-36-X, 2001, pp. 203-208.
3. Z. Zhang, J. Li, C Manikopoulos, J. Jorgenson, and J. Ucles, ``A Hierarchical Anomaly Network Intrusion Detection System Using Neural Network Classification", Advances in Neural Networks and Applications, N. Mastorakis (Ed.), World Scientific and Engineering Society Press, ISBN: 960-8052-26-2, 2001, pp. 333-338.
4. Z. Zhang, C. Manikopoulos, J. Jorgenson, ``Representation and Reduction of Network Intrusion Detection Data'', WSEAS Transactions on Communications, Issue 1, Vol. 1,July 2002, pp. 47-52.
5. Z. Zhang, C. Manikopoulos, J. Jorgenson, ``Experimental Comparisons of Binning Schemes in Representing Network Intrusion Detection Data'', Proceedings of the 36th Annual Conference on Information Science and Systems (CISS2002), Princeton University, Princeton, NJ, March 20-22, 2002.
6. Z. Zhang, J. Li, C. Manikopoulos, J. Jorgenson, J. Ucles, ``HIDE: a hierarchical network intrusion detection system using statistical preprocessing and neural network classification", Proceedings of the 2001 IEEE Workshop on Information Assurance and Security United States Military Academy, West Point, NY, 5-6 June, 2001.
I have taught a wide range of mathematics and mathematics-related courses, including, but not limited to, the following: Geometry for Middle School teachers; Arithmetic for Middle School teachers; Geometry of Art and Design; College algebra; Pre-Calculus; Calculus I, II, III; Numerical Analysis; Probability Theory; Financial Mathematics I, II; Modern Algebra; Analytic number theory; Statistics; Applied probability and statistics; Ordinary differential equations; Partial differential equations; Stochastic differential equations; Real Analysis; Riemann surfaces and trace formulas; Spectral theory and explicit formulas; and others.