Certain <i>L</i>²-Norms on Automorphic Representations of <i>SL</i>(2, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>)

Abstract

Let Γ be a non-uniform lattice in SL(2,R). In this paper, we study various L2-norms of automorphic representations of SL(2,R). We bound these norms with intrinsic norms defined on the representation. Comparison of these norms can help us understand the growth of L-functions in a systematic way.

Keywords

• authomorphic forms
• R %22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> automorphic representation over <named-content content-type="inline-formula"> <mml:math id="mm901"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> </mml:semantics> </mml:math> </named-content>
• <i>SL</i>(2)
• Iwasawa decomposition
• Fourier coefficients
• <i>K</i>-invariant norm