Mathematical Sciences: Arithmetic of Automorphic Forms on   Unitary Groups in Three Variables
{'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 will concentrate on the study of arithmetic                  aspects of automorphic forms on a unitary group G in three                      variables with respect to a CM extension E/F.  Three related                    topics will be investigated.  The first is an investigation of                  the coefficients in the Fourier-Jacobi expansion of a holomorphic               automorphic form on G which is an eigenfunction of all Hecke                    operators.  The coefficients, which are theta functions on an                   abelian variety with complex multiplication by E, are determined                by the eigenvalues of the Hecke operators, but no explicit                      formula is known.  It is suggested that the coefficients are                    related to special values of L-functions.  The second topic                     concerns the study of automorphic forms on G and their Fourier-                 Jacobi expansions over rings of integers.  The third topic is an                investigation of the Galois representations associated to                       automorphic representations of G.                                                    This research will concentrate on those areas of number                    theory concerning automorphic forms of many variables and abelian               varieties.  The former are functions which encode much of the                   information on the number theoretic problem to be solved allowing               one to use the powerful techniques of analysis in the solution.                 The latter are geometric objects which are relevant to the number               theory problem.  Together these objects form powerful tools to                  solve the very deep problems of number theory.  This P.I. is a                  master of these tools and so much of great interest will result                 from this research.
{'FirstName': 'Jonathan', 'LastName': 'Rogawski', 'PI_MID_INIT': 'D', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Jonathan D Rogawski', 'EmailAddress': 'jonr@math.ucla.edu', 'NSF_ID': '000453846', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of California-Los Angeles', 'CityName': 'LOS ANGELES', 'ZipCode': '900244200', 'PhoneNumber': '3107940102', 'StreetAddress': '10889 WILSHIRE BLVD STE 700', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '36', 'CONGRESS_DISTRICT_ORG': 'CA36', 'ORG_UEI_NUM': 'RN64EPNH8JC6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA, LOS ANGELES', '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': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8703288.xml'}