A relationship between the nonexistence of generalized bent functions and class groups  

作　　者：LIU FengMei 1,& YUE Qin 21 Department of Information Research,College of Information Engineering,Information Engineering University,Zhengzhou 450002,China 2 Department of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China 

出　　处：《Science China Mathematics》2010年第1期213-222,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10771100,10971250)

摘　　要：A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations. At the same time,a method is given which can be used to simplify the known results. Then we give the bounds and the meaning in algebraic number theory of the parameters in our results.A new result on the nonexistence of generalized bent functions is presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations. At the same time,a method is given which can be used to simplify the known results. Then we give the bounds and the meaning in algebraic number theory of the parameters in our results.

关 键 词：GENERALIZED BENT function INTEGRAL BASIS class group GENUS theory 

分 类 号：O177.4[理学—数学]