Mathematical Sciences: Automorphic Forms and Representation Theory
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle', 'PO_EMAI': None, 'PO_PHON': None}
This research deals with the subject of automorphic forms                  and representation theory using geometric methods.  The main                    problem is to obtain the analytic continuation and functional                   equation of the Hasse-Weil zeta function of Shimura varieties.                  The object is to express these zeta functions in terms of                       automorphic L-functions.  Then one must obtain the transformation               laws for these automorphic L-functions.                                              This research will study the generating functions for the                  number of solutions of systems of polynomial equations modulo all               the primes.  The properties of these functions will give an                     immense amount of information concerning the solution to the                    corresponding set of Diophantine Equations.  Number Theory has as               one of its chief components the study of Diophantine Equations,                 that is the solution of sets of equations in integers.
{'FirstName': 'Thomas', 'LastName': 'Hales', 'PI_MID_INIT': 'C', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Thomas C Hales', 'EmailAddress': 'hales@pitt.edu', 'NSF_ID': '000425934', 'StartDate': '12/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Harvard University', 'CityName': 'CAMBRIDGE', 'ZipCode': '021385366', 'PhoneNumber': '6174955501', 'StreetAddress': '1033 MASSACHUSETTS AVE STE 3', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MA05', 'ORG_UEI_NUM': 'LN53LCFJFL45', 'ORG_LGL_BUS_NAME': 'PRESIDENT AND FELLOWS OF HARVARD COLLEGE', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8715402.xml'}