Calculation of the Ramanujan $\tau$-Dirichlet series
HTML articles powered by AMS MathViewer
- by Robert Spira PDF
- Math. Comp. 27 (1973), 379-385 Request permission
Abstract:
A method is found for calculating the Ramanujan $\tau$-Dirichlet series $F(s)$. An inequality connecting points symmetric with the critical line, $\sigma = 6$, is proved, and a table is given for $\Gamma (s)F(s)$ for $\sigma = 6.0,6.5,t = 0(.25) 16$. Two zeros are found in $0 < t \leqq 16$; they appear to be simple and on the critical line.References
- G. H. Hardy, Ramanujan. Twelve lectures on subjects suggested by his life and work, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1940. MR 0004860
- Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
- T. M. Apostol and Abe Sklar, The approximate functional equation of Hecke’s Dirichlet series, Trans. Amer. Math. Soc. 86 (1957), 446–462. MR 94319, DOI 10.1090/S0002-9947-1957-0094319-3
- R. D. Dixon and Lowell Schoenfeld, The size of the Riemann zeta-function at places symmetric with respect to the point ${1\over 2}$, Duke Math. J. 33 (1966), 291–292. MR 190103, DOI 10.1215/S0012-7094-66-03333-3
- J. Barkley Rosser, Explicit remainder terms for some asymptotic series, J. Rational Mech. Anal. 4 (1955), 595–626. MR 72969, DOI 10.1512/iumj.1955.4.54021
- Bruce C. Berndt, On the zeros of a class of Dirichlet series. I, Illinois J. Math. 14 (1970), 244–258. MR 268363
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 379-385
- MSC: Primary 65D20
- DOI: https://doi.org/10.1090/S0025-5718-1973-0326995-4
- MathSciNet review: 0326995