This research will focus mainly on two areas. The first concerns congruences for values of L-functions predicted by the theory of multiplicative Galois structures. The second concerns the connections between Arakelov theory and adelic capacity theory. Work will also continue on determining the smallest arithmetic hyperbolic three manifold with a given number of cusps and to study whether the minimal volume of all hyperbolic manifolds with a given number of cusps is achieved by an arithmetic manifold. Finally, the connections between Mahler measures, L-series and K-groups of rings of integers will be studied This research will encompass broad areas of number theory and related areas. It will move into areas of analysis, algebra and geometry. The connections between all three areas will focused upon giving this research a particular appeal. Much of great interest will come from three endeavors.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
8814768
Program Officer
Ann K. Boyle
Project Start
Project End
Budget Start
1988-07-01
Budget End
1989-12-31
Support Year
Fiscal Year
1988
Total Cost
$42,950
Indirect Cost
Name
Barnard College
Department
Type
DUNS #
City
New York
State
NY
Country
United States
Zip Code
10027