Abstract
Let N be real, N≧5, write s = σ+it, and put
Work supported in part by National Science Foundation Grant MCS76-10346.
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References
T. Apostol, Sets of values taken by Dirichlet’s L-series. Proc. Sympos. Pure Math., vol. 8, Amer. Math. Soc. (Providence, R. I., 1965) pp. 133-137.
H. Bohr, Zur Theorie der allgemeinen Dirichletschen Reihen, Math. Ann., 79 (1919), 136–156.
G. Halász, On the distribution of additive and the mean values of multiplicative arithmetic functions, Studia Sci. Math. Hungar., 6 (1971), 211–233.
C. B. Haselgrove, A disproof of a conjecture of Pólya, Mathematika 5 (1958), 141–145.
N. Levinson, Asymptotic formula for the coordinates of the zeros of sections of the zeta function, ζN(s), near s=1, Proc. Nat. Acad. Sci. USA, 70(1973), 985–987.
R. Spira, Zeros of sections of the zeta function, I, II, Math. Comp., 20 (1966), 542–550; 22 (1968), 168-73.
P. Turán, On some approximative Dirichlet-polynomials in the theory of the zeta-function of Riemann, Danske Vid. Selsk. Mat.-Fys. Medd., 24 (1948), no. 17, 36 pp.
P. Turán, Nachtrag zu meiner Abhandlung “On approximative Dirichlet polynomials in the theory of zeta-function of Riemann”, Acta Math. Acad. Sci. Hungar., 10 (1959), 277–298.
P. Turán, A theorem on diophantine approximation with application to Riemann zeta-function, Acta Sci. Math. Szeged, 21 (1960), 311–318.
P. Turán, Untersuchungen über Dirichlet-Polynome, Bericht von der Dirichlet-Tagung, Akademie-Verlag (Berlin, 1963) pp. 71-80.
S. M. Voronin, On the zeros of partial sums of the Dirichlet series for the Riemann zeta-function, Dokl. Akad. Nauk Sssr, 216 (1974), 964–967; trans. Soviet Math. Doklady, 15 (1974), 900-903.
N. Wiener and A. Wintner, Notes on Pólya’s and Turán’s hypotheses concerning Liouville’s factor, Rend. Circ. Mat. Palermo, (2) 6 (1957), 240–248.
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Montgomery, H.L. (1983). Zeros of approximations to the zeta function. In: Erdős, P., Alpár, L., Halász, G., Sárközy, A. (eds) Studies in Pure Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5438-2_42
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DOI: https://doi.org/10.1007/978-3-0348-5438-2_42
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