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On the Zeros of Riemann’s Zeta-Function on the Critical Line

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Abstract

The present paper is a detailed exposition of the author’s report delivered at the International Sympozium in Memory of Hua Loo Keng, Beijing, on August the 6th, 1988.

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References

  1. L.K.Hua, On Tarry ‘s problem, Quart J. Math,Oxford Ser. 9(1938), 315–320.

    Google Scholar 

  2. L.K.Hua, On the number of solutions of Tarry ‘s Problem, Acta Sci. Sinica 1(1952), 1–76.

    Google Scholar 

  3. L.K.Hua. On Tarry’s problem, Third All-Union Math Congr. (Moscow, 1956 ), Vol. IV. Izdat Akad. Nauk. SSSR, Moscow, 1959,140–143 (Russian).

    Google Scholar 

  4. Arhibov, G. I., Karatsuba, A. A, Cubarekov, V. N., Proof of the convergence of singular integral of the Tarry problem, Dbkh AH SSSR,1979, T. 248, No.2, 268–272.

    Google Scholar 

  5. Arhibov, G. I., Karatsuba, A. A., Cubarekov, V. N., Trigonometrical integrals, Izv. AH SSSR, Ser. Math, 1979,T.43,No.5,971–1003.

    Google Scholar 

  6. Arhibov, G. I., Karatsuba, A. A., Cubarekov, V.N., Multiple Trigonometrical Sums,Tiyd.MIAH,1980,T.151.

    Google Scholar 

  7. Arhibov, G. I., Karatsuba, A. A., Cubarekov, V. N., Theory of multiple Trigonometrical Sums, Moscow, `Science“, 1987.

    Google Scholar 

  8. Occkokkov, K. I., I. M. Vinogradov ‘s series and integrals and their applications, Tiyd, MIAH, 1989.

    Google Scholar 

  9. Osckolkov, K. I., On properties of a class of I. M. Vinogradov’s series, Dbkl. AH SSSR,T.300, 1988, 803–807.

    Google Scholar 

  10. Arhibov, G. I., Ockolkov, K. I., On a class of Trigonometrical sum and its applications, Math. sb.,T.134,10,1987,147–157.

    Google Scholar 

  11. Ockolkov, K.I., On Spectral uniform convergence, Dokl. AH SSSR,T.288, No.1, 1986, 54–58.

    Google Scholar 

  12. Ockolkov, K. I., On continuous function with polynomial spectrum, See `Investigations on the theory of approximations of functions“, BFAH,SSSR, 1987,187–200.

    Google Scholar 

  13. Riemann, G. F. B., Selected works, M, OGIZ, 1948.

    Google Scholar 

  14. Hardy, G. H., Sur les zeros de la fonction C (s) de Riemann, Conpt. Rend. Acad. Sci., 1914, v. 158, 1012–1014.

    Google Scholar 

  15. Landau, E., Über die Hardysche Eutdeckung unendlich vieler Nullstellen der Zeta-function mit reelen Teil 1/2, Math. Ann.,1915,b.76212– 243.

    Google Scholar 

  16. Hardy, G. H., Littlewood, J. E., Contributions to the theory of Riemann zata-function and the theory of distribution of primes, Acta Math., 1918, v.41,119–196.

    Google Scholar 

  17. Hardy, G. H., Littlewood, J. E., The zeros of Riemann ‘s zeta-function and the critical line, Math. Zs.,1921,v.10,283–317.

    Google Scholar 

  18. Selberg, A., On the zeros of Riemann ‘s zeta-function, Ski.. Norske Vid. Akad. Oslo, 1942, V. 10.

    Google Scholar 

  19. Levinson, N., More than one third of the zeros of Riemann’s zeta-function are on o=1 /2, Adv. in Math.,1974, v.13, 383–436.

    Google Scholar 

  20. Mozer, Ja., On a theorem of Hardy-Littlewood in the theory of Riemann zeta function, Acta Arith,31, 1976,45–51.

    Google Scholar 

  21. Mozer, Ja., improved theorems of Hardy-Littlewood on the density of zeros of the function C Acta Math,Univ. Comen. Britislava, 42–43, 1983, 41–50.

    Google Scholar 

  22. Karatsuba, A. A., On distance between consecutive zeros of Riemann zeta function lying on the critical line, Dokl. AH SSSR, 272, 6,1983,1312–1314.

    Google Scholar 

  23. Karatsuba, A. A., On zeros of Riemann zeta function on an interval of the critical line, Dokl. AH SSSR, 272, 1983, 1312–1314.

    Google Scholar 

  24. Ivic, A., Topics in recent zeta-function theory, Publ. Math. d’Orsay, Universite Paris-Sud, Orsay, 1983.

    Google Scholar 

  25. Karatsuba, A. A., On zeros of the function C (s) on certain interval of the critical line, Izv. AH SSSR. Ser. Mat. 48, 1984, 569–584.

    Google Scholar 

  26. Karatsuba, A. A., On distribution of zeros of C. AH SSSR, Ser. Mat. 48, 1984, 1214–1224.

    Google Scholar 

  27. Karatsuba, A. A., On zeros of the function C (s) on the neighbourhood of the critical line, Izv. AH SSSR, Ser. Mat. 49, 1985, 326–333.

    Google Scholar 

  28. Ivic, A., On a problem connected with zeros of C (s) on the critical line, MI:. Math. 1987,104 17– 27.

    Google Scholar 

  29. Karatsuba. A. A., Riemann zeta function and its zeros, YMH,40, 1985, 19–70.

    Google Scholar 

  30. Titchmarsh, E. K., Theory of Riemann zeta function, M.: EL, 1953.

    Google Scholar 

  31. Karatsuba,A.A., On real zeros of the function Cit I, YMH,40, 1985,171–172.

    Google Scholar 

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Authors

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Sheng Gong Qi-Keng Lu Yuan Wang Lo Yang

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© 1991 Springer-Verlag Berlin Heidelberg

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Karatsuba, A.A. (1991). On the Zeros of Riemann’s Zeta-Function on the Critical Line. In: Gong, S., Lu, QK., Wang, Y., Yang, L. (eds) International Symposium in Memory of Hua Loo Keng. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07981-2_7

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  • DOI: https://doi.org/10.1007/978-3-662-07981-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-07983-6

  • Online ISBN: 978-3-662-07981-2

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