Let $S_k$ be the space of holomorphic cusp forms of weight $k$ with respectto $SL_2(mathbb{Z})$. Let $f in S_k$ be a normalized Hecke eigenform,$L_f(s)$ the $L$-function attached to the form $f$. In this paper we considerthe distribution of zeros of $L_f(s)$ in the strip $sigma leq Re s leq 1$for fixed $sigma>1/2$ with respect to the imaginary part. We study estimatesof [ N_f(sigma,T) = #{hoinmathbb{C} mid L_f(ho)=0, sigma leqReho leq 1, 0 leq Imho leq T} ] for $1/2 leq sigma leq1$ and large$T>0$. Using the methods of Karatsuba and Voronin we shall give another prooffor Ivi'{c}'s method.
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机译:设$ S_k $为权重$ k $的全纯尖点形式相对于$ SL_2( mathbb {Z})$的空间。令S_k $中的$ f为归一化的Hecke本征形式,$ L_f(s)$附加到形式$ f $的$ L $函数。在本文中,对于固定$ sigma> 1/2 $,我们考虑$ L_f(s)$的零点在$ sigma leq Re s leq 1 $相对于虚部的分布。我们研究 [N_f( sigma,T)=# { rho in mathbb {C} mid L_f( rho)= 0, sigma leq Re rho leq 1,0 leq的估计 Im rho leq T} ]为$ 1/2 leq sigma leq1 $和large $ T> 0 $。使用唐津法和沃罗宁的方法,我们将对伊维{c}的方法给出另一种证明。
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