Calculation of the Ramanujan -Dirichlet series

Author:
Robert Spira

Journal:
Math. Comp. **27** (1973), 379-385

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1973-0326995-4

MathSciNet review:
0326995

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Abstract: A method is found for calculating the Ramanujan -Dirichlet series . An inequality connecting points symmetric with the critical line, , is proved, and a table is given for for . Two zeros are found in ; they appear to be simple and on the critical line.

**[1]**G. H. Hardy,*Ramanujan. Twelve lectures on subjects suggested by his life and work*, Cambridge University Press, Cambridge, England; Macmillan Company, New York, 1940. MR**0004860****[2]**Milton Abramowitz and Irene A. Stegun,*Handbook of mathematical functions with formulas, graphs, and mathematical tables*, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR**0167642****[3]**T. M. Apostol and Abe Sklar,*The approximate functional equation of Hecke’s Dirichlet series*, Trans. Amer. Math. Soc.**86**(1957), 446–462. MR**0094319**, https://doi.org/10.1090/S0002-9947-1957-0094319-3**[4]**R. D. Dixon and Lowell Schoenfeld,*The size of the Riemann zeta-function at places symmetric with respect to the point 1\over2*, Duke Math. J.**33**(1966), 291–292. MR**0190103****[5]**J. Barkley Rosser,*Explicit remainder terms for some asymptotic series*, J. Rational Mech. Anal.**4**(1955), 595–626. MR**0072969****[6]**Bruce C. Berndt,*On the zeros of a class of Dirichlet series. I*, Illinois J. Math.**14**(1970), 244–258. MR**0268363**

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DOI:
https://doi.org/10.1090/S0025-5718-1973-0326995-4

Article copyright:
© Copyright 1973
American Mathematical Society