Mathematical Sciences: Automorphic Forms on GL(r) and the   Metaplectic Groups
{'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 focus on the theory of automorphic forms                on the metaplectic groups.  It will attempt to show that L-                     functions associated with Dirichlet characters of order n occur                 as Fourier coefficients of Eisenstein series on the n-fold covers               of GL(n).  This result would have applications to analytic number               theory and to the formulation of the proper generalization of                   Waldspurger's theorem.  It will further attempt to show that the                Euler product associated with an automorphic form on the n-fold                 cover of SL(r) is the Rankin-Selberg convolution of the form with               a theta function on the n-fold cover of GL(n).  Also it will                    attempt to show that the Fourier coefficients of an Eisenstein                  series on the n-fold cover of GL(r+1) are Rankin-Selberg                        convolutions of the form with theta functions on the n-fold cover               of GL(n-1).  Also Bump will investigate automorphic forms and L-                functions on the exceptional group G2.  Finally work will be done               on the higher convolutions of nonramified Whittaker functions on                GL(r,R) from the point of view of generalized Barnes' lemmas and                generalized hypergeometric series.                                                   This research is in the area of automorphic forms, a branch                of number theory wherein number theoretic functions are encoded                 into complex analytic functions allowing the deep tools of                      analysis to come to bear on the number theory problems.  This                   idea is generalized in many ways and has proved to be a                         fundamental tool in many areas.  Multivariable generalizations                  are the focus of this research and Bump is a leader in this                     direction.  The results of this research will prove to be very                  exciting.
{'FirstName': 'Daniel', 'LastName': 'Bump', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Daniel Bump', 'EmailAddress': 'bump@math.stanford.edu', 'NSF_ID': '000435746', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Stanford University', 'CityName': 'STANFORD', 'ZipCode': '943052004', 'PhoneNumber': '6507232300', 'StreetAddress': '450 JANE STANFORD WAY', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '16', 'CONGRESS_DISTRICT_ORG': 'CA16', 'ORG_UEI_NUM': 'HJD6G4D6TJY5', 'ORG_LGL_BUS_NAME': 'THE LELAND STANFORD JUNIOR UNIVERSITY', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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