Mathematical Sciences: The Arithmetic and Analysis of       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 is divided into three parts.  The first part                 concerns automorphic forms that arise as determinants of elliptic               operators on certain manifolds.  Ways of obtaining GL(n) analogs                of theta and other elliptic functions which are of arithmetic                   interest will be studied.  Also studied will be symplectic                      automorphic forms recently discovered in mathematical physics as                well as Selberg zeta functions in higher rank spaces.  In the                   second part, the existence problem of cusp forms for co-finite                  subgroups of SL(2,R) with special emphasis on the family of Hecke               groups will be studied.  In this area a conjectural spectral                    theoretic characterization of arithmetic groups as well as a                    criterion that should distinguish congruence and non-congruence                 subgroups will be investigated.  The third part of this research                will be devoted to the interplay between cusp forms on GL(n) and                Kloosterman sums.  Possible connections between certain                         automorphic objects such as Kloosterman zeta functions and Hecke                polynomials and certain infinite sums and products attached to                  Kloosterman sums in algebraic geometry will be described.                            This research will concentrate on the theory of automorphic                forms.  These are complex analytic functions which lead to great                insights into number theory.  They encode basic number theoretic                information, allowing the powerful tools of modern analysis to                  help solve fundamental problems in number theory.  This area is                 one of the very most important in mathematics today and this                    young investigator has done much already done much of importance                in it.  Further important results will surely result from this                  current grant.
{'FirstName': 'Isaac', 'LastName': 'Efrat', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Isaac Efrat', 'EmailAddress': 'efrat@math.umd.edu', 'NSF_ID': '000164543', 'StartDate': '07/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Columbia University', 'CityName': 'NEW YORK', 'ZipCode': '100277922', 'PhoneNumber': '2128546851', 'StreetAddress': '615 W 131ST ST', 'StreetAddress2': 'MC 8741', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'NY13', 'ORG_UEI_NUM': 'F4N1QNPB95M4', 'ORG_LGL_BUS_NAME': 'THE TRUSTEES OF COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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