This award supports the research in Automorphic Forms of Professor Paul Garrett of the University of Minnesota. Dr. Garrett's work is concerned with integral representations of L- functions and Eisenstein series. Among the topics he plans to work on are: criteria for expressibility of automorphic forms as theta series, relations between zeros and poles of Eisenstein series and L-functions, integral representations of Eisenstein series attached to cuspforms, and uniqueness results for Hecke eigenfunctions with prescribed invariance. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of Modular and Automorphic Forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of Geometry and Analysis, it retains connection to its historical roots.
