Abstract
We prove that the functional equation , for t in
with d odd, admits a nonzero solution f if
with a, b positive integers such that
and
mod 4. The proof involves theta functions on elliptic curves with complex multiplication.
2010 Mathematics Subject Classification:
Acknowledgments
I thank Gérard Laumon, Samuel Lelièvre and Emmanuel Ullmo for enlighting discussions on this project.
Notes
1 With other “classical” notations for theta functions as in [Citation3], one has the equalities, and