A Burgess-like subconvex bound for twisted L-functions
A Burgess-like subconvex bound for twisted L-functions
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DOI：
10.1515/forum.2007.003
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发表时间：
2007-01
期刊：
影响因子：
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通讯作者：
V. Blomer;G. Harcos;P. Michel;Z. Mao
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文献类型：
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作者：
V. Blomer;G. Harcos;P. Michel;Z. Mao
摘要设g为任意能级和任意形态的反转新形式（全纯或质量），χ为导体q的原始特征，s为临界线上的点。证明了，其中ε >是任意的，θ =是目前已知的对Ramanujan-Petersson猜想的近似（允许θ = 0）；此外，对s和g的所有参数的依赖是多项式的。这个结果是Dirichlet l -函数的Burgess经典次凸界的一个类比。在附录2中，我们将上述结果与Waldspurger的一个定理和Baruch-Mao的阿德里奇计算相结合，得到了全纯半积分权顶点形式的傅里叶系数的一个改进的一致上界。
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.