Number Theoretic Computations
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Several problems in Classical Number Theory are considered.                in which interest has been renewed due to the availability of                   computers.  The problems chosen are highly interactive with the                 computational practice.  In the theory of Hilbert modular forms                 and functions, the algebraic system needed for handling double                  Fourier series has produced achievements and limitations, both                  reflected in the theory.  In the problem of defining number                     fields as governed by class number, the discovery of theorems                   through experimentation has been so empirical yet routine that                  some expert logic system is called for.  In the problem of                      establishing the euclidean algorithm by tiling the hypercube, the               proofs by analytic computation are a difficult simulation of what               is conceptually a graphic method which is yet to be developed.                  In all these cases and others, improvements in hardware and                     software would be interactive with both the quality and direction               of the theory.
{'FirstName': 'Harvey', 'LastName': 'Cohn', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Harvey Cohn', 'EmailAddress': None, 'NSF_ID': '000456936', 'StartDate': '09/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '126400', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}, {'Code': '127100', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
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