让 f (z) 是为 SL 2 的一种 Hecke-Maass 尖顶形式() ,并且让 L (s, f ) 相应自形的 L 功能被联系到 f。为足够地大的 T,让 N (, T ) 是零的数字 L 的 =+i (s, f ) 与|T,,零根据复合正在被数。在这份报纸,我们为 3/4 得到那 1...让 f (z) 是为 SL 2 的一种 Hecke-Maass 尖顶形式() ,并且让 L (s, f ) 相应自形的 L 功能被联系到 f。为足够地大的 T,让 N (, T ) 是零的数字 L 的 =+i (s, f ) 与|T,,零根据复合正在被数。在这份报纸,我们为 3/4 得到那 1,在那里存在经常的 C =C() 以便 N (, T ) T 2 (1 )/(logT ) C,它改进以前的结果。展开更多
Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Gene...Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Generalized Ramanujan Conjecture(GRC),the author gives the generalized prime number theorem for L(s,π×■) when π≌π'.The result generalizes the corresponding result of Liu and Ye in 2007.展开更多
Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central character.Its Hecke eigenvalue λπ(n)is a real multiplicative function in n.We show that λπ(n)<0 for some ...Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central character.Its Hecke eigenvalue λπ(n)is a real multiplicative function in n.We show that λπ(n)<0 for some n<<Q^(2/5)_(π),where Qπdenotes(a special value of)the analytic conductor.The value 2/5 is the first explicit exponent for Hecke-Maass newforms.展开更多
Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symm...Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.展开更多
基金The author would like to thank Xu Zhao and the referees for carefully reading the manuscript and detailed comments. This work was supported by the National Natural Science Foundation of China (Grant No. 11126151) and the Scientific Foundation of Henan University (Grant No. 2012YBZR030).
文摘让 f (z) 是为 SL 2 的一种 Hecke-Maass 尖顶形式() ,并且让 L (s, f ) 相应自形的 L 功能被联系到 f。为足够地大的 T,让 N (, T ) 是零的数字 L 的 =+i (s, f ) 与|T,,零根据复合正在被数。在这份报纸,我们为 3/4 得到那 1,在那里存在经常的 C =C() 以便 N (, T ) T 2 (1 )/(logT ) C,它改进以前的结果。
文摘Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Generalized Ramanujan Conjecture(GRC),the author gives the generalized prime number theorem for L(s,π×■) when π≌π'.The result generalizes the corresponding result of Liu and Ye in 2007.
基金supported by General Research Fund of the Research Grants Council of Hong Kong(Grant Nos.17313616 and 17305617)supported by National Natural Science Foundation of China(Grant No.11871193)+1 种基金the Program for Young Scholar of Henan Province(Grant No.2019GGJS026)supported by National Natural Science Foundation of China(Grant No.11871344)。
文摘Letπbe a self-dual irreducible cuspidal automorphic representation of GL_(2)(A_(Q))with trivial central character.Its Hecke eigenvalue λπ(n)is a real multiplicative function in n.We show that λπ(n)<0 for some n<<Q^(2/5)_(π),where Qπdenotes(a special value of)the analytic conductor.The value 2/5 is the first explicit exponent for Hecke-Maass newforms.
基金supported by the National Natural Science Foundation of China(No.11301142)the Key Project of Colleges and Universities of Henan Province(No.15A110014)
文摘Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.