The second moment of symmetric square L-functions over Gaussian integers

The Second Moment of Quadratic Twists of Modular L-functions

The family of quadratic twists of a modular form has received much attention in recent years. Motivated by the Birch-Swinnerton-Dyer conjectures, we seek an understanding of the central values of the associated L-functions, and while this question has been investigated extensively, much remains unknown. One important theme in this area concerns the moments of these central L-values. Thanks to t...

The Second Moment of Dirichlet Twists of Hecke L-functions

A Note on the Second Moment of Automorphic L-functions

We obtain the formula for the twisted harmonic second moment of the L-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the reciprocity formula for the twisted second moment of Dirichlet L-functions.

On Non-vanishing of Symmetric Square L-functions

We find a lower bound in terms of N for the number of newforms of weight k and level N whose symmetric square L-functions are non-vanishing at a fixed point s0 with 1 2 < Re(s0) < 1 or s0 = 1 2 .

Averages of symmetric square L-functions, and applications

We exhibit a spectral identity involving L(s,Symf) for f on SL2. Perhaps contrary to expectations, we do not treat L(s,Symf) directly as a GL3 object. Rather, we take advantage of the coincidence that the standard L-function for SL2 is the symmetric square for a cuspform on GL2 restricted to SL2. [1] As SL2 = Sp2, the integral identities obtained from Sp2n × Sp2n ⊂ Sp4n produce standard L-funct...