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On large values of the function S(t) on short intervals

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Abstract

We prove a theorem on upper and lower bounds for the argument S(t) of the Riemann zeta function on short intervals of the critical line.

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References

  1. M. A. Korolev, “On large values of the function S(t) on short intervals,” Izv. Ross. Akad. Nauk Ser. Mat. 69(1), 113–122 (2005) [Russian Acad. Sci. Izv.Math. 69 (1), 115–124 (2005)].

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  2. É. Trost, Prime Numbers (Fizmatgiz, Moscow, 1959) [in Russian].

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  3. A. A. Karatsuba and M. A. Korolev, “The argument of the Riemann zeta function,” Uspekhi Mat. Nauk 60(3), 41–96 (2005) [RussianMath. Surveys 60 (3), 433–488 (2005)].

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    R. N. Boyarinov

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  1. R. N. Boyarinov
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Correspondence to R. N. Boyarinov.

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Original Russian Text © R. N. Boyarinov, 2011, published in Matematicheskie Zametki, 2011, Vol. 89, No. 4, pp. 495–502.

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Boyarinov, R.N. On large values of the function S(t) on short intervals. Math Notes 89, 472–479 (2011). https://doi.org/10.1134/S0001434611030187

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  • DOI: https://doi.org/10.1134/S0001434611030187

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