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On the bounded term in the mean square formula for the approximate functional equation of ζ2(s)

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References

  1. A.Ivić, The Riemann zeta-function. New York 1985.

  2. A. Ivić, Power moments of the error term in the approximate functional equation for ζ2(s). Acta Arith.65, 137–145 (1993).

    Google Scholar 

  3. A. Ivić andI. Kiuchi, On some integrals involving the Riemann zeta-function in the critical strip. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat.5, 19–28 (1994).

    Google Scholar 

  4. M. Jutila, On the approximate functional equation for ζ2(s) and other Dirichlet series. Quart. J. Math. Oxford Ser. (2)37, 193–209 (1986).

    Google Scholar 

  5. I. Kiuchi, On an exponential sum involving the arithmetic functionσ a(n). Math. J. Okayama Univ.29, 193–205 (1987).

    Google Scholar 

  6. I. Kiuchi, An improvement on the mean value formula for the approximate functional equation of the square of the Riemann zeta-function. J. Number Theory45, 312–319 (1993).

    Google Scholar 

  7. I. Kiuchi, The mean value formula for the approximate functional equation of ζ2(s) in the critical strip. Arch. Math.64, 316–322 (1995).

    Google Scholar 

  8. I. Kiuchi andK. Matsumoto, Mean value results for the approximate functional equation of the square of the Riemann zeta-function. Acta Arith.61, 337–345 (1992).

    Google Scholar 

  9. K. Matsumoto, The mean square of the Riemann zeta-function in the strip 1/2<σ <1 (in Japanese). Sûrikaiseki Kenkyûsho Kôkyûroku837, 150–163 (1993).

    Google Scholar 

  10. K. Matsumoto andT. Meurman, The mean square of the Riemann zeta-function in the critical strip II. Acta Arith.68, 369–382 (1994).

    Google Scholar 

  11. K. Matsumoto andT. Meurman, The mean square of the Riemann zeta-function in the critical strip III. Acta Arith.64, 357–382 (1993).

    Google Scholar 

  12. T. Meurman, On the mean square of the Riemann zeta-function. Quart. J. Math. Oxford Ser. (2)38, 337–343 (1987).

    Google Scholar 

  13. Y. Motohashi, A note on the approximate functional equation for ζ2(s). Proc. Japan Acad. Ser. A Math. Sci.59, 393–396 (1983).

    Google Scholar 

  14. Y. Motohashi, A note on the approximate functional equation for ζ2(s) II. Proc. Japan Acad. Ser. A Math. Sci.59, 469–472 (1983).

    Google Scholar 

  15. Y.Motohashi, Lectures on the Riemann-Siegel formula. Ulam Seminar, Colorado University 1987.

  16. E. Preissmann, Sur la moyenne quadratique du terme de reste du probléme du cercle. C. R. Acad. Sci. Paris Sér I. Math.306, 151–154 (1988).

    Google Scholar 

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  1. Kohji Matsumoto

    Present address: Department of Mathematics Faculty of Education, Iwate University, Ueda, 020, Morioka, Japan

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    Matsumoto, K. On the bounded term in the mean square formula for the approximate functional equation of ζ2(s). Arch. Math 64, 323–332 (1995). https://doi.org/10.1007/BF01198087

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