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}
}
  • T. Oliver
  • Published 2013
  • Mathematics
  • Journal of The Mathematical Society of Japan
  • 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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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 31 REFERENCES
    Two-Dimensional Adelic Analysis and Cuspidal Automorphic Representations of GL(2)
    5
    A Polya-Hilbert operator for automorphic L-functions and a local trace formula
    6
    Analysis on arithmetic schemes. II
    10
    Mean-periodicity and zeta functions
    10
    Adelic approach to the zeta function of arithmetic schemes in dimension two
    15
    On a representation of the idele class group related to primes and zeros of L-functions
    42
    WHERE STANDS FUNCTORIALITY TODAY
    35
    Positivity of certain functions associated with analysis on elliptic surfaces
    8
    A spectral interpretation for the zeros of the Riemann zeta function
    15