Mathematical Sciences: Mean Values and Zeros of Dirichlet   Series
{'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}
The purpose of this research is to investigate a number of                 open problems concerning the distribution of zeros and the mean                 values of Dirichlet series.  The first problem is to prove                      asymptotic mean value estimates for Dirichlet polynomials whose                 lengths are much longer than the interval of integration or, in                 the case of discrete means, than the range of summation.  An                    immediate application of such results is to the study of gaps                   between zeros of the Riemann Zeta function.  The second problem                 is to show that certain functions defined by a Dirichlet series                 have a functional equation like that of the Riemann Zeta function               and have infinitely many zeros off the critical line, but still                 have a positive proportion of their zeros on it.  The third                     problem is to widen the range of application of the pair                        correlation method and thereby establish (conditional) mean value               estimates for the zeta function and arithmetical functions that                 have so far been unobtainable.  Another problem is to obtain                    asymptotic estimates for fractional moments of the zeta function.               The approach envisioned will require some kind of assumption on                 the vertical distribution of zeros.  The final problem is to                    study the distribution of zeros of the zeta functions attached to               function fields.
{'FirstName': 'Steven', 'LastName': 'Gonek', 'PI_MID_INIT': 'M', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Steven M Gonek', 'EmailAddress': 'gonek@math.rochester.edu', 'NSF_ID': '000323114', 'StartDate': '07/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Rochester', 'CityName': 'ROCHESTER', 'ZipCode': '146113847', 'PhoneNumber': '5852754031', 'StreetAddress': '910 GENESEE ST', 'StreetAddress2': 'STE 200', 'CountryName': 'United States', 'StateName': 'New York', 'StateCode': 'NY', 'CONGRESSDISTRICT': '25', 'CONGRESS_DISTRICT_ORG': 'NY25', 'ORG_UEI_NUM': 'F27KDXZMF9Y8', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ROCHESTER', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1264', 'Text': 'ALGEBRA,NUMBER THEORY,AND COM'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8805800.xml'}