NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF MARYLAND, COLLEGE PARK
Initial Amendment Date:	May 8, 1990
Latest Amendment Date:	March 10, 1992
Award Number:	9003109
Award Instrument:	Continuing Grant
Program Manager:	William Y. Velez DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	June 1, 1990
End Date:	November 30, 1993 (Estimated)
Total Intended Award Amount:	$80,350.00
Total Awarded Amount to Date:	$80,350.00
Funds Obligated to Date:	FY 1990 = $25,600.00 FY 1991 = $26,900.00 FY 1992 = $27,850.00
History of Investigator:	Stephen Kudla (Principal Investigator) ssk@math.umd.edu
Recipient Sponsored Research Office:	University of Maryland, College Park 3112 LEE BUILDING COLLEGE PARK MD  US  20742-5100 (301)405-6269
Sponsor Congressional District:	04
Primary Place of Performance:	DATA NOT AVAILABLE
Primary Place of Performance Congressional District:
Unique Entity Identifier (UEI):	NPU8ULVAAS23
Parent UEI:	NPU8ULVAAS23
NSF Program(s):	ALGEBRA,NUMBER THEORY,AND COM
Primary Program Source:
Program Reference Code(s):
Program Element Code(s):	126400
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

This award supports the research in automorphic forms of Professor Steven Kudla of the University of Maryland at College Park. Dr. Kudla's project is to work on two problems involving theta functions, L-functions, and arithmetic. The first of these problems concerns a conjecture about the identification of the first two terms in the Laurent expansion of the Siegel Eisenstein series at certain special points. The second is concerned with an analogue for the triple L-function of the result of Gross and Zagier that relates the derivative of the standard L-function of a holomorphic cusp form on GL(2) to the height pairing of Heegner points on the Jacobian of the modular curve. 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.

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