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An asymptotic formula in the theory of numbers

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References

  1. Carlitz, L.: Note on a paper of Götze. Math. Nach.35, 289–294 (1967)

    Google Scholar 

  2. Estermann, T.: On an asymptotic formula due to Titchmarsh. J. London Math. Soc.6, 250–257 (1931)

    Google Scholar 

  3. Gallagher, P. X.: The large sieve. Mathematika14, 14–20 (1967)

    Google Scholar 

  4. Hardy, G. H., Wright, E. M.: An Introduction to the Theory of Numbers. 4th ed. London: Oxford Univ. Press 1960

    Google Scholar 

  5. Hooley, C.: An asymptotic formula in the theory of numbers. Proc. London Math. Soc.7, 396–413 (1957)

    Google Scholar 

  6. Indlekofer, K. H.: Eine asymptotische Formel in der Zahlentheorie. Arch. Math.23, 619–624 (1972)

    Google Scholar 

  7. Ingham, A. E.: Some asymptotic formulae in the theory of numbers. J. London Math. Soc.2, 202–208 (1927)

    Google Scholar 

  8. Landau, E.: Handbuch der Verteilung der Primzahlen. New York: Chelsea 1953

    Google Scholar 

  9. Linnik, J. V.: The dispersion method in binary additive problems. Trans. Math. Mono.4, Providence, Amer. Math. Soc. 1963

  10. Motohashi, Y.: An asymptotic formula in the theory of numbers. Acta Arith.16, 255–264 (1970)

    Google Scholar 

  11. Motohashi, Y.: On the distribution of prime numbers which are of the formx 2+y 2+1. Acta Arith.16, 351–363 (1970)

    Google Scholar 

  12. Niven, I., Zuckermann, H.: An introduction to the theory of numbers. 3rd ed. New York: Wiley 1972

    Google Scholar 

  13. Pracher, K.: Primzahlverteilung. Berlin, Heidelberg, Göttingen: Springer 1957

    Google Scholar 

  14. Rankin, R. A.: Contributions to the theory of Ramanujan's function τ(n) and similar arithmetical functions, I. Proc. Cambridge Phil. Soc.35, 351–356 (1939)

    Google Scholar 

  15. Rankin, R. A.: An Ω result for the coefficients of cusp forms. Math. Ann.203, 239–250 (1973)

    Google Scholar 

  16. Rankin, R. A., Rushforth, J. M.: The coefficients of certain integral modular forms. Proc. Cambridge Phil. Soc.50, 305–308 (1954)

    Google Scholar 

  17. Ramanujan, S.: Some formulae in the analytic theory of numbers. Mess. Math.45, 81–84 (1915)

    Google Scholar 

  18. Titchmarsh, E. C.: The theory of the Riemann zeta function. Oxford: Claredon Press 1951

    Google Scholar 

  19. Vinogradov, A. I.: On the density conjecture for DirichletL-series. Izv. Akad. Nauk SSSR Ser. Mat.29, 903–934 (1965)

    Google Scholar 

  20. Wolke, D.: Über das summatorische Verhalten zahlentheoretischer Funktionen. Math. Ann.194, 147–166 (1971)

    Google Scholar 

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Some of the results in this paper appeared in the author's Ph. D. dissertation written under the direction of Professor Bruce C. Berndt at the University of Illinois in 1975.

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Redmond, D. An asymptotic formula in the theory of numbers. Math. Ann. 224, 247–268 (1976). https://doi.org/10.1007/BF01459848

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