# Automorphicity and mean-periodicity

@article{Oliver2013AutomorphicityAM, title={Automorphicity and mean-periodicity}, author={T. Oliver}, journal={Journal of The Mathematical Society of Japan}, year={2013}, volume={69}, pages={25-51} }

If C is a smooth projective curve over a number eld k, then, under fair hy- potheses, itsL-function admits meromorphic continuation and satises the anticipated functional equation if and only if a related function is X-mean-periodic for some appropriate functional space X. Building on the work of Masatoshi Suzuki for modular elliptic curves, we will explore the dual relationship of this result to the widely believed conjecture that such L-functions should be automorphic. More precisely, we will… CONTINUE READING

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