Marvin I. Knopp

Research Interests: Number Theory. Modular Forms. Special Functions.

I am a member of the Editorial Board of the Ramanujan Journal, and a reviewer for Mathematical Reviews and Zentralblatt fur Mathematik.

My latest papers are:

On vector-valued modular forms and their Fourier coefficients, submitted (with G. Mason).

Generalized modular forms. J. Number Theory 99 (2003), no. 1, pp. 1-28. (with Geoffrey Mason)

Sums of squares and the preservation of modularity under congruence restrictions. In: Symbolic computation, number theory, special functions, physics and combinatorics (Gainesville, FL, 1999), 59-71, Dev. Math., 4, Kluwer Acad. Publ., Dordrecht, 2001. (with Paul Bateman and Boris Datskovsky)

Easy proofs of Riemann's functional equation for zeta(s) and of Lipschitz summation. Proc. Amer. Math. Soc. 129 (2001), no. 7, 1915-1922 (with Sinai Robins)

Hamburger's theorem on zeta(s) and the abundance principle for Dirichlet series with functional equations (invited paper), in Number Theory, Indian National Science Academy, New Delhi, eds.: R.P. Bambah et al. (2000) 201-216.

The Hecke convergence factor and modular forms of weight zero, in The Mathematics of Leon Ehrenpreis, Contemporary Mathematics, vol 251, American Mathematical Society, Providence, eds.: E. Grinberg et al. (2000) 371-391 (with W. Pribitkin).

On Dirichlet series satisfying Riemann's functional equation, Inventiones Math, 117 (1994), 361-372.

Ph.D. students directed:

Kenneth Stolarsky (presently at University of Illinois, Urbana): Higher partition functions and their relation to finitely generated nilpotent groups, 1967.

Douglas Niebur (Lockheed-Martin): Automorphic integrals of arbitrary positive dimension and Poincare series, 1968.

Mark Sheingorn (Baruch College, CUNY): Poincare series of polynomials bounded away from zero on a fundamental region, 1970.

David James (University of Michigan, Dearborn): Automorphic forms on domains larger than the upper half-plane and factors of automorphy, 1970.

Alayne Parson(Ohio State University): Generalized Kloosterman sums and the Fourier coefficients of cusp forms, 1973.

Shlomo Libeskind (The University of Oregon): A development of a unit on number theory for use in high school, based on a heuristic approach, 1971.

Richard Cavaliere (St. Joseph's University, Philadelphia): On rational period functions and modular integrals, 1984.

Young-ju Choie (Pohang Institute of Technology, Korea): Rational period functions for the modular group, with poles in an arbitrary quadratic field, 1986.

Sr. Ann Heath (Immaculata College, Paoli, PA): The Hecke-Weil correspondence in the context of modular integrals, 1993.

Kevin Flood (Moravian College, Bethlehem, PA): The Hecke-Weil correspondence in the context of modular integrals, 1993.

Wendell Culp-Ressler (Franklin and Marshall College, Lancaster, PA): The Hecke correspondence for modular integrals on the full modular group, 1994.

Wladimir Pribitkin (Princeton University): On the Fourier coefficients of modular forms of small positive weights, 1995.

Abdul Hassen (Rowan University, Camden, NJ): Modular integrals whose periods are log-polynomial sums, 1996.

Paul Pasles (Villanova University, Philadelphia, PA): Nonanalytic automorphic integrals on the Hecke groups, 1997.

Kurt E. Ludwick (Salisbury University, Salisbury, MD): Congruence restricted modular forms, 2001.

Daniel T. Russo (Dickinson College, Carlisle, PA): Hecke-Weil correspondence on conjugate groups, 2002.

Omer Yayenie (Murray State University, Kentucky): Hyperbolic convexity of a standard fundamental domain of a subgroup of a Hecke discrete group, 2003.