AN EXERCISE CONCERNING THE SELFDUAL CUSP FORMS ON GL(3)

作者：Ramakrishnan Dinakar^*

来源：Indian Journal of Pure and Applied Mathematics, 2014, 45(5): 777-785.

DOI：10.1007/s13226-014-0088-1

• Selfdual representations
• automorphic forms
• symmetric square
• adjoint

Using L-functions and various known results, we provide a proof of the following:
Let F be a number field and Pi a cuspidal automorphic form on GL(3)/F which is selfdual. Then, up to replacing Pi by a quadratic twist, it can be realized as the adjoint of a cusp form pi on GL(2)/F, with pi unraruified at any prime where H is; We also investigate the properties of pi when II is regular and algebraic.

• 出版日期2014-10