Dennis Arnold Hejhal (born December 10, 1948 in Chicago) is an American mathematician. In his mathematical research he frequently uses extensive computer calculation.
Hejhal graduated from the University of Chicago in 1970 with a bachelor's degree and from Stanford University in 1972 with a PhD in mathematics under the direction of Menahem Max Schiffer. He became an assistant professor at Harvard, then in 1974 an associate professor at Columbia University and starting in 1978 a professor at the University of Minnesota, where he now works. Additionally he has been since 1994 a professor at the University of Uppsala and since 1986 a fellow of the Minnesota Supercomputing Institute. He was in 1993 a guest professor at Princeton University and several times (for the first time in 1983) at the Institute for Advanced Study.
Hejhal works on analytic number theory, automorphic forms, the Selberg trace formula and quantum chaos. In 1967 he was a Putnam Fellow, from 1972 to 1974 a Sloan Fellow. In 1986 he was an invited speaker at the International Congress of Mathematicians in Berkeley (Zeros of Epstein Zeta Functions and Supercomputers). In 1997 he received the Goran Gustafson Prize from the Swedish Academy of Sciences and in 2005 the Eva and Lars Gårding Prize. He is a member of the Swedish Royal Society of Sciences. In 2012 he became a fellow of the American Mathematical Society.
- Theta functions, kernel functions and abelian integrals, AMS 1972
- Eigenvalues of the Laplacian for Hecke triangle groups, AMS 1992
- Regular b-Groups, degenerating Riemann surfaces and spectral theory, AMS 1990
- The Selberg Trace Formula for PSL (2, R), 2 volumes, Springer, 1976, 1983 (3rd volume planned)
- Editor with Peter Sarnak, Audrey Terras: The Selberg Trace Formula and related topics, AMS 1986 (Conference, Bowdoin College 1984)
- Editor with Martin Gutzwiller, Andrew Odlyzko, et al.. Emerging applications of Number theory, Springer 1999
- "The Mathematical Association of America's William Lowell Putnam Competition". Retrieved 27 March 2017.
- List of Fellows of the American Mathematical Society, retrieved January 19, 2013.
- Patterson, S. J. (1978). "Review: Dennis A. Hejhal, The Selberg trace formula for PSL(2, R), Volume I". Bull. Amer. Math. Soc. 84 (2): 256–260. doi:10.1090/s0002-9904-1978-14466-8.