Super-positivity of a family of L-functions in the level aspect
Super-positivity of a family of L-functions in the level aspect
复制标题
L-函数族在能级方面的超正性
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Bingrong Huang
中科院分区：
文献类型：
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作者：
D. Goldfeld;Bingrong Huang
一个自守自对偶L-函数具有超正性，如果完备L-函数在中心点s = 1/2处的所有导数非负，且在真实的点s> 1/2处的所有导数为正.本文证明了至少有12%的与权为2且大素水平q的Hecke基尖点形式相关的L-函数具有超正性。本文还证明了至少有49%的L-函数在$$ mathrm{Re}（s）> 0$$Re（s）>0上没有真实的零点，除了可能在$$s = 1/2.$$ s=1/2。
An automorphic self dual L-function has the super-positivity property if all derivatives of the completed L-function at the central point $$s=1/2$$s=1/2 are nonnegative and all derivatives at a real point $$s > 1/2$$s>1/2 are positive. In this paper, we prove that at least 12% of L-functions associated to Hecke basis cusp forms of weight 2 and large prime level q have the super-positivity property. It is also shown that at least 49% of such L-functions have no real zeros on $$ mathrm{Re}(s) > 0$$Re(s)>0 except possibly at $$s = 1/2.$$s=1/2.