Subconvexity for Half Integral Weight $L$-functions
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ID: 283364
2013
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Abstract
We prove a subconvexity bound in the conductor aspect for $L(s,f,\chi)$ 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.
| Reference Key |
kiral2013subconvexity
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| Authors | Eren Mehmet Kiral |
| Journal | arXiv |
| Year | 2013 |
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