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A Burgess-like subconvex bound for twisted L-functions
-
V Blomer
,
G Harcos
Published/Copyright:
February 21, 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. In Appendix 2 the above result is combined with a theorem of Waldspurger and the adelic calculations of Baruch–Mao to yield an improved uniform upper bound for the Fourier coefficients of holomorphic half-integral weight cusp forms.
Received: 2004-11-23
Published Online: 2007-02-21
Published in Print: 2007-01-29
© Walter de Gruyter
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Articles in the same Issue
- Solving Abstract Cauchy Problems with closable operators in reflexive spaces via resolvent-free approximation
- Chain transitive sets for flows on flag bundles
- A Burgess-like subconvex bound for twisted L-functions
- On recurrence in zero dimensional flows
- Solutions of nonlinear elliptic equations in unbounded Lipschitz domains
- π∗(L2T(1)/(v1)) and its applications in computing π∗(L2T(1)) at the prime two
- A proof of the Livingston conjecture
- Expectations of hook products on large partitions and the chi-square distribution
