Mathematical Sciences: Value Distribution of Complex        Functions
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Two of the main objectives of this work in the mathematical                theory of entire and meromorphic functions are to give sharp                    bounds for the sum of Nevanlinna deficiencies of a meromorphic                  function and to analyze the minimum modulus of an entire                        function.  The deficiency of a meromorphic function is a measure                of the function's affinity for a given complex number.  Generally               the deficiency is infinite, that is, meromorphic functions                      achieve most complex values infinitely often.  For functions of                 finite order the sum of the defects is known to be no greater                   than two.  The amount this falls short of two should be measured                in terms of the order of the function.  The conjectured upper                   bounds (proposed many years ago by Albert Edrei) have been proved               to be valid for large subclasses of functions.  There is                        considerable evidence to suggest that a complete solution of this               fundamental estimate may be near at hand.                                            The second thrust of this project seeks to compare the                     maximum and minimum moduli of entire (or subharmonic) functions                 of prescribed order.  The moduli are compared for large values of               the underlying variable.  When the order of the function is less                than one, the classic result of Wiman-Valiron gives a sharp lower               bound.  For order equal to unity or above little exact                          information is known.  New, related, results may provide                        information related to this question.  The focus of the research                will be on relating the number and distribution of zeros to the                 extremal cases.  This work is expected to have ancillary                        applications to complex differential equations and quasiconformal               mapping.
{'FirstName': 'David', 'LastName': 'Drasin', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'David Drasin', 'EmailAddress': 'drasin@math.purdue.edu', 'NSF_ID': '000216952', 'StartDate': '06/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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