On Fourier Coefficients of the Symmetric Square L-Function at Piatetski-Shapiro Prime Twins
نویسندگان
چکیده
Let Pc(x)={p?x|p,[pc]areprimes},c?R+?N and ?sym2f(n) be the n-th Fourier coefficient associated with symmetric square L-function L(s,sym2f). For any A>0, we prove that mean value of over Pc(x) is ?xlog?A?2x for almost all c??,(5+3)/8?? in sense Lebesgue measure. Furthermore, it holds c?(0,1) under Riemann Hypothesis. obtain asymptotic formula ?f2(n) ?p,qprimep?x,q=[pc]?f2(p)=xclog2x(1+o(1)), c??,(5+3)/8??, where ?f(n) normalized a holomorphic cusp form f full modular group.
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ژورنال
عنوان ژورنال: Mathematics
سال: 2021
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math9111254