Subconvexity for Half Integral Weight L-functions
Kiral, Eren Mehmet
Original · EN
We prove a subconvexity bound in the conductor aspect for L(s,f,χ) where f is a half integer weight modular form. This L-function has analytic continuation and functional equation, but no Euler product. Due to the lack of an Euler product, one does not expect a Riemann hypothesis for half integer weight modular forms. Nevertheless one may speculate a Lindelof-type hypothesis, and this current subconvexity result is an indication towards its truth.
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