Mathematical Sciences: Theory of P-Adic Modular Forms and   Hecke Algebras
{'Code': '03040300', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Gary Cornell', 'PO_EMAI': None, 'PO_PHON': None}
The research in this grant concerns the theory of p-adic                   Hecke algebras.  This theory attempts to give a systematic way to               construct p-adic L-functions associated with p-adic or complex                  cusp forms and their Galois representations over power series                   rings with coefficients in the p-adic integers.  Also the                       principal investigator hopes to find arithmetic relations between               these Galois representations and the constructed p-adic L-                      functions.  This theory has been developed for the rational                     numbers but much remains to be done over general number fields.                 There will be applications to the Iwasawa theory of imaginary                   quadratic fields.                                                                    The p-adic theory of modular forms is the subject of this                  research.  Modular forms are functions that transform in certain                ways and are at the center of much research in number theory                    today.  The p-adic theory replaces the usual real or complex                    numbers with the number theoretic p-adic numbers.  Obtaining                    analogs with the usual theory is a major focus of this research.
{'FirstName': 'Haruzo', 'LastName': 'Hida', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Haruzo Hida', 'EmailAddress': 'hida@math.ucla.edu', 'NSF_ID': '000203692', 'StartDate': '07/01/1988', '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}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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