Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on the mean value of the zeta and $L$-functions, I

Yoichi Motohashi

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 61, Number 7 (1985), 222-224.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195514645

Digital Object Identifier
doi:10.3792/pjaa.61.222

Mathematical Reviews number (MathSciNet)
MR816718

Zentralblatt MATH identifier
0573.10027

Subjects
Primary: 11M06: $\zeta (s)$ and $L(s, \chi)$

Citation

Motohashi, Yoichi. A note on the mean value of the zeta and $L$-functions, I. Proc. Japan Acad. Ser. A Math. Sci. 61 (1985), no. 7, 222--224. doi:10.3792/pjaa.61.222. https://projecteuclid.org/euclid.pja/1195514645


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References

  • [1] F. V. Atkinson: The mean value of the Riemann zeta-function. Acta Math., 81, 353-376 (1949).
  • [2] D. R. Heath-Brown: An asymptotic series for the mean value of Dirichlet L-functions. Comment. Math. Helv., 56, 148-161 (1981).

See also

  • Part II: Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, II. Proc. Japan Acad. Ser. A Math. Sci., Volume 61, Number 10 (1985), 313--316.
  • Part III: Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, III. Proc. Japan Acad. Ser. A Math. Sci., Volume 62, Number 4 (1986), 152--154.
  • Part IV: Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, IV. Proc. Japan Acad. Ser. A Math. Sci., Volume 62, Number 8 (1986), 311--313.
  • Part V: Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, V. Proc. Japan Acad. Ser. A Math. Sci., Volume 62, Number 10 (1986), 399--401.
  • Part VI: Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, VI. Proc. Japan Acad. Ser. A Math. Sci., Volume 65, Number 8 (1989), 273--275.
  • Part VII: Aleksandar Ivić, Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, VII. Proc. Japan Acad. Ser. A Math. Sci., Volume 66, Number 6 (1990), 150--152.
  • Part VIII: Yoichi Motohashi. A note on the mean value of the zeta and $L$-functions, VIII. Proc. Japan Acad. Ser. A Math. Sci., Volume 70, Number 6 (1994), 190--193.