Quantitative non-vanishing of central values of certain L-functions on $${{\text {GL}}}(2)\times {{\text {GL}}}(3)$$
نویسندگان
چکیده
Let $$\phi $$ be an even Hecke–Maass cusp form on $${{\text {SL}}}_2({\mathbb {Z}})$$ whose L-function does not vanish at the center of functional equation. In this article, we obtain exact formula average triple products , f and $${\bar{f}}$$ where runs over orthonormal basis $$H_k$$ Hecke eigen elliptic forms a fixed weight $$k\geqslant 4$$ . As application, prove quantitative non-vanishing results central values for family degree 6 L-functions $$L(s,\phi \times \mathrm{Ad}\,f)$$ with in union $$(\mathrm{K}\leqslant k<2\mathrm{K})$$ as $$\mathrm{K}\rightarrow \infty
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2022
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-021-02886-5