Mathematical Sciences: Topics in Arithmetic Theory of       Quadratic Forms
{'Code': '03040300', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Ann K. Boyle'}
This research concerns the arithmetic theory of quadratic                  forms.  In particular there will be special emphasis on the                     classification and representation problems of positive definite                 forms.  With respect to the classification theory the Principal                 Investigator will investigate both the explicit and complete                    determination of certain genera as well as the relationships                    between even unimodular quadratic forms over integers of a number               field and their algebraic descents.  In the area of                             representation of quadratic forms he will study primitive                       representations of n-ary forms by positive definite m-ary                       quadratic forms and representations of binary forms by certain                  positive quaternary quadratic forms.                                                 Quadratic forms are homogeneous polynomials in many                        variables of degree two.  This research concerns the number                     theory problems which arise in determining which integers can be                values of them when integer are substituted for their variables.                Classifying quadratic forms in classes that all have the same                   values and representing the forms by simpler forms are valuable                 tools in answering this problem.
{'FirstName': 'John', 'LastName': 'Hsia', 'EmailAddress': None, 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Ohio State University Research Foundation -DO NOT USE', 'CityName': 'Columbus', 'ZipCode': '432101016', 'PhoneNumber': '6146888734', 'StreetAddress': '1960 KENNY RD', 'CountryName': 'United States', 'StateName': 'Ohio', 'StateCode': 'OH'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8803805.xml'}