Automorphic Forms on GL(2)
Automorphic Forms on GL(2)
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DOI：
10.1007/bfb0058988
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发表时间：
1970
期刊：
影响因子：
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通讯作者：
R. Langlands
中科院分区：
文献类型：
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作者：
R. Langlands
两个最著名的赫克的成就是他的理论LL-职能grössencharakter，这是狄利克雷级数可以表示的欧拉产品，他的理论欧拉产品相关的自守形式的GL（2）。由于格形性是GL（1）上的自守形式，人们不禁要问，与GL（2）上自守形式相关联的欧拉积在数论中所起的作用是否与具有格形性的L函数所起的作用相似。特别是，它们与与伽罗瓦群的二维表示相关联的Artin L函数的关系与Hecke的Artin L函数的关系相同。
Two of the best known of Hecke's achievements are his theory of LL-functions with grössencharakter, which are Dirichlet series which can be represented by Euler products, and his theory of the Euler products associated to automorphic forms on GL (2). Since a grössencharakter is an automorphic form on GL (1) one is tempted to ask if the Euler products associated to automorphic forms on GL (2) play a role in the theory of numbers similar to that played by the L-functions with grössencharakter. In particular do they bear the same relation to the Artin L functions associated to two-dimensionalrepresentations of a Galois group as the Hecke the Artin L-