Common zeros of theta functions and central Hecke L-values of CM number fields of degree 4

Yang, Tonghai

doi:10.1090/S0002-9939-98-04213-0

Common zeros of theta functions and central Hecke L-values of CM number fields of degree 4
HTML articles powered by AMS MathViewer

by Tonghai Yang PDF

Proc. Amer. Math. Soc. 126 (1998), 999-1004 Request permission

Abstract:

In this note, we apply the method of Rodriguez Villegas and Yang (1996) to construct a family of infinite many theta series over the Hilbert-Blumenthal modular surfaces with a common zero. We also relate the non- vanishing of the central L-values of certain Hecke characters of non-biquadratic CM number fields of degree 4 to the nonvanishing of theta functions at CM points in the Hilbert-Blumenthal modular surfaces.

References

David E. Rohrlich, Root numbers of Hecke $L$-functions of CM fields, Amer. J. Math. 104 (1982), no. 3, 517–543. MR 658544, DOI 10.2307/2374152
David E. Rohrlich, Galois conjugacy of unramified twists of Hecke characters, Duke Math. J. 47 (1980), no. 3, 695–703. MR 587174
F. Rodriguez Villegas and T. H. Yang, Central values of Hecke L-functions of CM number fields, submitted to Duke Math. J., 1996.
Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Kanô Memorial Lectures, No. 1, Iwanami Shoten Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Publications of the Mathematical Society of Japan, No. 11. MR 0314766
Ken Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp. 62 (1994), no. 206, 899–921. MR 1218347, DOI 10.1090/S0025-5718-1994-1218347-3