Proceedings of the Japan Academy, Series A, Mathematical Sciences

Transcendency of zeros of Eisenstein series

Naruo Kanou

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The Eisenstein series of heigher weight has at least one transcendental zero point on upper half plane.

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Proc. Japan Acad. Ser. A Math. Sci., Volume 76, Number 5 (2000), 51-54.

First available in Project Euclid: 23 May 2006

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Primary: 11F11: Holomorphic modular forms of integral weight

Number theory modular forms transcendental numbers


Kanou, Naruo. Transcendency of zeros of Eisenstein series. Proc. Japan Acad. Ser. A Math. Sci. 76 (2000), no. 5, 51--54. doi:10.3792/pjaa.76.51.

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  • Rankin, F. K. C., and Swinnerton-Dyer, H. P. F.: On the zeros of Eisenstein series. Bull. London. Math. Soc., 2, 169–170 (1970).
  • Atkin, A. O. L.: Note on a paper of Rankin. Bull. London. Math. Soc., 1, 191–192 (1969).
  • Siegel, C. L.: Transcendental Numbers. Princeton Univ. Press, Princeton (1949).
  • Shimura, G.: Introduction to the arithmetic theory of automorphic functions. Iwanami Shoten, Tokyo and Princeton Univ. Press, Princeton (1971).
  • Serre, J. P.: Cours D'Arithmétique. Presses Univ. de France, Paris (1970).
  • Washington, L. C.: Introduction to Cyclotomic Fields. Springer-Verlag, New York (1982).
  • Borcherds, R. E.: Automorphic forms on $O_{s+2, 2}(\mathbf{R})$ and infinite products. Invent. Math., 120, 161–213 (1995). f