The main objects of study in this article are two classes of Rankin-SelbergL-unctions, namely L(s, f \times g) and L(s, sym^2(g) \times sym^2(g)), wheref, g are newforms, holomorphic or of Maass type, on the upper half plane, andsym^2(g) denotes the symmetric square lift of g to GL(3). We prove that ingeneral, i.e., when these L-functions are not divisible by L-functions ofquadratic characters (such divisibility happening rarely), they do not admitany Landau-Siegel zeros. These zeros, which are real and close to s=1, arehighly mysterious and are not expected to occur. There are corollaries of ourresult, one of them being a strong lower bound for special value at s=1, whichis of interest both geometrically and analytically. One also gets this way agood bound on the norm of sym^2(g).
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机译：本文的主要研究对象是两类Rankin-SelbergL-连接，即L（s，f \ times g）和L（s，sym ^ 2（g）\ times sym ^ 2（g）），其中f ，g是上半平面上的全同型或Maass型的新形式，sym ^ 2（g）表示g对GL（3）的对称平方提升。我们证明一般地说，即当这些L函数不能被二次方字符的L函数整除（这种除数很少发生）时，它们就不会接受Landau-Siegel零。这些零是实数且接近s = 1，非常神秘，并且预计不会出现。我们的结果有一些推论，其中之一是s = 1时特殊值的强下界，这在几何和分析上都很有趣。人们也以这种方式对sym ^ 2（g）的范数进行了很好的约束。
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