My Research

My research uses number-theoretic methods as well as harmonic and complex analysis in developing new theorems. My most recent efforts have been concentrated in the area of zeta functions and spectral theory. I often use computers as a means of obtaining insight as to what should be true here. (I have been a Fellow in the Minnesota Supercomputer Inst since the late 1980's.)

The following is a list of my books published. They are available in major libraries.

TITLE:Theta functions, kernel functions, and Abelian integrals, by Dennis A. Hejhal.
IMPRINT: [Providence R.I., American Mathematical Society, 1972] 112 p. 26 cm.

TITLE:Eigenvalues of the Laplacian for Hecke triangle groups / Dennis A. Hejhal. Hecke triangle groups.
IMPRINT:Providence, RI : American Mathematical Society, 1992. 165 p.

TITLE:Regular b-groups, degenerating Riemann surfaces, and spectral theory / Dennis A. Hejhal.
IMPRINT:Providence, R.I., USA : American Mathematical Society, 1990. iv, 138 p. : ill. ; 26 cm.

TITLE:AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on the Selberg Trace Formula and Related Topics (1984 : Bowdoin College)
The Selberg trace formula and related topics : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 22-28, 1984 with support from the National Science Foundation / Dennis A. Hejhal, Peter Sarnak, and Audrey Anne Terras, editor.
IMPRINT:Providence, R.I. : American Mathematical Society, c1986. ix, 554 p. ; 25 cm.

TITLE:The Selberg trace formula for PSL (2, IR) / Dennis A. Hejhal.
IMPRINT:Berlin ; New York : Springer-Verlag, 1976-1983. 2 v. ; 25 cm.

My papers on line
A list of all my publications is available in PDF format
Computer Images:
Click to view some on-line quantum chaos computer graphics generated by my research groups in Minnesota and Uppsala using supercomputers (e.g., Cray YMP-EL, T3D, T3E, C90).
Group members:
Barry N. Rackner
James Z. Wang

Some Links:

Number Theory Web
[an error occurred while processing this directive]