As a part of the behavior function extension and the humanities characteristic, product is an entity performance that integrates the technique and culture. In the article, the inherent relation between technique and c...As a part of the behavior function extension and the humanities characteristic, product is an entity performance that integrates the technique and culture. In the article, the inherent relation between technique and culture of products is analyzed to reveal the cultural mode of product development from the view of human society development in industry design. These will not only contribute to analyze the relation between notional technique characteristics and humanity, but also help to study the products developed under the inter-relation between life and environment.展开更多
Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this ...Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,Mk（q,f）=∑χ（mod q）χ≠χ0｜L（1/2,f χ）｜^2k〈〈 kФ（q）（log q）^k^2, and the result also holds for any real number 0 〈 k 〈 1 under the GRH for L（s, f χ）.The authors also prove that under the GRH for L（s, f χ）,for any real number k 〉 0 and any large prime q.展开更多
文摘As a part of the behavior function extension and the humanities characteristic, product is an entity performance that integrates the technique and culture. In the article, the inherent relation between technique and culture of products is analyzed to reveal the cultural mode of product development from the view of human society development in industry design. These will not only contribute to analyze the relation between notional technique characteristics and humanity, but also help to study the products developed under the inter-relation between life and environment.
基金supported by the National Natural Science Foundation of China(No.11301299)the Natural Science Foundation of Shandong Province(No.ZR2012AQ001)the Specialized Research Fund for the Doctoral Program of Higher Education(New Teachers)(Nos.20110131120001,20120131120075)
文摘Let f（z） be a holomorphic cusp form of weight κ with respect to the full modular group SL2（Z）. Let L（s, f） be the automorphic L-function associated with f（z） and χ be a Dirichlet character modulo q. In this paper, the authors prove that unconditionally for k =1/n with n ∈ N,Mk（q,f）=∑χ（mod q）χ≠χ0｜L（1/2,f χ）｜^2k〈〈 kФ（q）（log q）^k^2, and the result also holds for any real number 0 〈 k 〈 1 under the GRH for L（s, f χ）.The authors also prove that under the GRH for L（s, f χ）,for any real number k 〉 0 and any large prime q.
