Simultaneous Non-Vanishing of Central Values of Twisted Maass L -Functions

Key Points

• The aim is to establish conditions under which central values of twisted L-functions do not vanish simultaneously.
• Calculated moments of twisted central L-values using advanced formulas.
• Applied a Waldspurger-type formula tailored for Maass cusp forms.
• Utilized the Kuznetsov trace formula relevant to the Kohnen subspace.
• Established a quantitative result showing simultaneous non-vanishing of central values for twisted L-functions.
• Provided conditions under which quadratically twisted L-functions associated with $SL(2, \\mathbb {Z})$ and $SL(3, \\mathbb {Z})$ remain non-zero.
• Demonstrated significance of the connection between the L-values and the properties of Maass cusp forms.