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

Jerzy Kaczorowski; Alberto Perelli

doi:10.4171/prims/53-2-5

JournalsprimsVol. 53, No. 2pp. 337–347

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

Jerzy Kaczorowski
Adam Mickiewicz University, Poznán, Poland
Alberto Perelli
Università di Genova, Italy

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Abstract

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.

Cite this article

Jerzy Kaczorowski, Alberto Perelli, A Weak Converse Theorem for Degree 2 $L$ -Functions with Conductor 1. Publ. Res. Inst. Math. Sci. 53 (2017), no. 2, pp. 337–347

DOI 10.4171/PRIMS/53-2-5