Mathematical Sciences: Eisenstein Series on the Metaplectic Group
{'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 proposed research is a continuation of joint work                      already begun with Dr. Daniel Bump and Dr. Jeffrey Hoffstein,                   which established nonvanishing results for certain L-functions                  arising in the theory of automorphic forms. Partial results along               these lines have already allowed Dr. Friedberg and his                          collaborators to conclude that when the L-function of an elliptic               curve defined over the rational numbers is nonzero at the value                 1, both the group of Q-rational points and the Tate-Shafarevich                 group of the elliptic curve are finite.                                              In algebraic geometry, a "curve" is what may be defined in                 the plane by a single polynomial equation in two variables. When                at least one of the monomials in this polynomial has total degree               three, and no monomials have higher degree; and when the                        resulting curve does not cross itself, the curve is called                      "elliptic". These curves, seemingly so simple, carry nonetheless                an astonishing amount of deep structure, and have been the basis                of farreaching conjectures of astonishing difficulty. Among these               conjectures are those made in the 1960's by Birch and Swinnerton-               Dyer, connecting values of certain functions to the structure of                elliptic curves. Dr. Friedberg's work is an essential part of the               recent verification of the first cases of the Birch and                         Swinnerton-Dyer Conjectures.
[{'FirstName': 'Geoffrey', 'LastName': 'Mason', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Geoffrey Mason', 'EmailAddress': 'gem@ucsc.edu', 'NSF_ID': '000296247', 'StartDate': '07/01/1989', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Solomon', 'LastName': 'Friedberg', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Solomon Friedberg', 'EmailAddress': 'friedber@bc.edu', 'NSF_ID': '000462876', 'StartDate': '07/01/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}]
{'Name': 'University of California-Santa Cruz', 'CityName': 'SANTA CRUZ', 'ZipCode': '950641077', 'PhoneNumber': '8314595278', 'StreetAddress': '1156 HIGH ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '19', 'CONGRESS_DISTRICT_ORG': 'CA19', 'ORG_UEI_NUM': 'VXUFPE4MCZH5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF CALIFORNIA SANTA CRUZ', '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=1988&All=true', 'xml': '8821762.xml'}