A Weak Converse Theorem for Degree 2 L-Functions with Conductor 1

作者：Kaczorowski Jerzy^*; Perelli Alberto

来源：Publications of the Research Institute for Mathematical Sciences, 2017, 53(2): 337-347.

DOI：10.4171/PRIMS/53-2-5

• L-functions
• Selberg class
• converse theorems
• cusp forms

We show that every normalized function of degree 2 and conductor 1 in the extended Selberg class has real coefficients, and certain invariants agree with those of the L-functions of cusp forms for the full modular group. The result may therefore be regarded as a weak converse theorem in such a general setting.

• 出版日期2017