The first moment of the symmetric-square L-function

✍ Scribed by Rizwanur Khan

• Book ID: 104024800
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 123 KB
• Volume: 124
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.09.010

✦ Synopsis

We find a twisted first moment of L(sym 2 f, s) at any point s on the critical line, over a basis of weight k Hecke eigenforms f for the full modular group, as k → ∞. As a corollary we show that given any point on the critical line and large enough even k, there exists an eigenform f of weight k such that L(sym 2 f, s) is nonvanishing at that point.