Let φ(n) denote the Euler-totient function, we study the distribution of solutions of φ(n) ≤ x in arithmetic progressions, where n ≡ l(mod q) and an asymptotic formula was obtained by Perron formula.
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
基金Supported by the National Natural Science Foundation of China（11271249） Supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission（1601213） Supported by the Scientific Research Program of Yangtze Normal University（2012XJYBO31）
文摘Let φ(n) denote the Euler-totient function, we study the distribution of solutions of φ(n) ≤ x in arithmetic progressions, where n ≡ l(mod q) and an asymptotic formula was obtained by Perron formula.
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.
