Mathematical Sciences: Poincare series and Automorphic Forms
{'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 Poincare series on GL(n).                Five specific projects will be undertaken.  The first is to use                 these GL(n) Poincare series to obtain information on GL(n)                      automorphic forms (zeroes of L-functions, large sieve coefficient               inequalities) and on sums of GL(n) Kloosterman sums.  The second                is to study the relation between this GL(n) Kuznietsov formula                  and two other trace formulas: the Selberg trace formula and the                 relative trace formula.  The third is to study Poincare series                  (and L-functions) on the exceptional groups.  The fourth is to                  obtain strong converse theorems on GL(3) twisting by only a                     finite number of characters and with explicit level.  The fifth                 is to study the spectral decomposition of the product of two                    automorphic forms as a first step towards understanding the                     decomposition of the tensor product of two automorphic                          representations into irreducible components under the action of                 the Hecke algebra.                                                                   This research will concentrate on one of the most active and               most important areas of analytic number theory, namely, the                     theory of automorphic forms.  Generalizing this valuable tool to                higher dimensions has proven to be both difficult and rewarding.                Many problems in number theory have been answered in this manner.               The P.I. has established himself as an expert in this area and                  will no doubt produce much of great interest in this grant                      period.
{'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': '07/01/1987', '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}
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{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701035.xml'}