Mathematical Sciences: Arithmetic Functions, Their Value    Distribution and Application to Algebra
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{'SignBlockName': 'Gary Cornell', 'PO_EMAI': None, 'PO_PHON': None}
This research concerns additive and multiplicative functions               in number theory.  They will be studied by augmenting the                       classical methods of Fourier analysis, sieve methods and                        exponential sums.  New ideas will be taken from functional                      analysis to apply to their study.  The functional analysis is to                be carried out in an infinite collection of finite dimensional                  spaces, in a uniform manner.  Besides allowing a re-                            interpretation of certain well-known results, such as the Turan-                Kubilius inequality, this approach offers methods and directions                for future development.                                                              Most of the classical functions in number theory, such as                  the number of divisors of an integer or the number of natural                   numbers less than an integer which are relatively prime to that                 integer, are what are called multiplicative functions.  This                    research will apply various tools from analysis and probability                 theory to study the general properties of such functions and the                closely related functions called additive functions.
{'FirstName': 'Peter', 'LastName': 'Elliott', 'PI_MID_INIT': 'D', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter D Elliott', 'EmailAddress': 'pdtae@euclid.Colorado.EDU', 'NSF_ID': '000419984', 'StartDate': '08/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
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