Faculty EmeritusEmeritus Selected Publications(with Y. Kitaoka, M. Kneser) Representations by positive definite quadratic forms, J. Reine Angew. Math. Vol. 301 (1978), pp. 129 - 140.(with P. J. Costello) Even unimodular 12-dimensional quadratic forms over Q(\sqrt{5}), Advances in Math. Vol. 64 (1987), pp. 241 - 278.(with D. R. Estes) Spinor genera under field extensions IV: Spinor class fields, Japanese J. Math. Vol. 16 (1990), pp. 341 - 350.(with M. J\"ochner) Almost strong approximation for definite quadratic spaces, Inventiones Math. Vol. 129 (1997), pp. 471 - 487.(with Y. Y. Shao, F. Xu) Representations of indefinite quadratic forms, J. Reine Angew. Math. Vol. 494 - M. Kneser's 70th birthday volume (1998), pp. 129 - 140.Arithmetic of indefinite quadratic forms, A.M.S. Contemporary Mathematics Vol. 249 (1999), pp. 1 - 15.(with W. K. Chan) On almost strong approximation for algebraic groups, Journal of Algebra Vol. 254 (2002), pp. 441 - 461. Areas of Expertise Number Theory & Algebraic Number Theory Algebraic Groups Combinatorial Coding & Design Theories Integral Quadratic Forms Modular Forms Education PhD: MIT (1966) Columbus