A Burgess-like subconvex bound for twisted L-functions

@inproceedings{Blomer2007ABS,
  title={A Burgess-like subconvex bound for twisted L-functions},
  author={Valentin Blomer and Gergely Harcos and Philippe Michel and Zhouhang Mao},
  year={2007}
}
Abstract Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, χ a primitive character of conductor q, and s a point on the critical line ℜs = ½. It is proved that , where ε > 0 is arbitrary and θ = is the current known approximation towards the Ramanujan–Petersson conjecture (which would allow θ = 0); moreover, the dependence on s and all the parameters of g is polynomial. This result is an analog of Burgess' classical subconvex bound for Dirichlet L-functions… 

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