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arXiv · 1307.0112

Subconvexity for Half Integral Weight $L$-functions

Eren Mehmet Kiral
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Abstract

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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Eren Mehmet Kiral. 2014-07-18. Subconvexity for Half Integral Weight $L$-functions. https://doi.org/10.1007/s00209-015-1504-x

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