Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on the approximate functional equation for $\zeta ^2 \left( s \right)$

Yoichi Motohashi

Full-text: Open access

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 59, Number 8 (1983), 393-396.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195515413

Digital Object Identifier
doi:10.3792/pjaa.59.393

Mathematical Reviews number (MathSciNet)
MR726533

Zentralblatt MATH identifier
0541.10032

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

Citation

Motohashi, Yoichi. A note on the approximate functional equation for $\zeta ^2 \left( s \right)$. Proc. Japan Acad. Ser. A Math. Sci. 59 (1983), no. 8, 393--396. doi:10.3792/pjaa.59.393. https://projecteuclid.org/euclid.pja/1195515413


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References

  • [1] G. H. Hardy and J. E. Littlewood: The approximate functional equation for C(e) and C2(s). Proc. London Math. Soc, (2) 29, 81-97 (1929).
  • [2] D. R. Heath-Brown: The fourth power moment of the Riemann zeta-function, ibid., (3) 38,385-422 (1979).
  • [3] C. Hooley: On the number of divisors of quadratic polynomials. Acta Math., 110, 97-114 (1963).
  • [4] M. Jutila: Transformation formulae for Dirichlet polynomials (to appear).
  • [5] E. C. Titchmarsh: The approximate functional equation for C2(s). Quart. J. Math. Oxford, 9, 109-114 (1938).
  • [6] E. C. Titchmarsh: The Theory of the Riemann Zeta-f unction. Oxford (1951).

See also

  • Part II: Yoichi Motohashi. A note on the approximate functional equation for $\zeta ^2 \left( s \right)$, II. Proc. Japan Acad. Ser. A Math. Sci., Volume 59, Number 10 (1983), 469--472.
  • Part III: Yoichi Motohashi. A note on the approximate functional equation for $\zeta ^2 \left( S \right)$, III. Proc. Japan Acad. Ser. A Math. Sci., Volume 62, Number 10 (1986), 410--412.