Average Values of Symmetric Square L - Functions at Re ( s ) = 2
نویسنده
چکیده
Let Lsym2(f)(s) be the symmetric square L-function associated to a newform of weight 2 and level N . For N prime, we will derive asymptotic formulae for the average values of Lsym2(f)(s) at a general point on the line Re(s) = 2 when f varies over the set of all normalized newforms. RÉSUMÉ: Soit Lsym2(f)(s) la fonction L du carré symétrique d’une forme primitive de poids 2 et niveau N . Pour N premier, on dérive une formule asymptotique pour les valeurs moyennes de Lsym2(f)(s) en un point général de la droite Re(s) = 2 et f variant dans l’ensemble des formes primitives normalisées.
منابع مشابه
Zeros of Families of Automorphic L-functions
For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g., because of the Dirichlet class-number formula) and the symmetric square L-functions of...
متن کاملZeros of Families of Automorphic L-functions Close to 1
For many L-functions of arithmetic interest, the values on or close to the edge of the region of absolute convergence are of great importance, as shown for instance by the proof of the Prime Number Theorem (equivalent to non-vanishing of ζ(s) for Re(s) = 1). Other examples are the Dirichlet L-functions (e.g. because of the Dirichlet class-number formula) and the symmetric square L-functions of ...
متن کاملOn 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 .
متن کاملOn the Complex Moments of Symmetric Power L-Functions
Investigations about the distribution of values of L-functions at s = 1 (in this paper, all Lfunctions are normalized so that the center of the critical strip is s = 1/2) began with the works of Chowla, and Chowla-Erdös in the case of L-functions associated to the family of real Dirichlet characters. Via Dirichlet’s class number formula, these have implications to the study of the distribution ...
متن کاملValues of symmetric cube L-functions and Fourier coefficients of Siegel Eisenstein series of degree-3
We obtain formulas for certain weighted sums of values of the symmetric square and triple product L-functions. As a consequence, we get exact values at the right critical point for the symmetric square and symmetric cube L-functions attached to certain cuspforms. We also give applications to Fourier coefficients of modular forms.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004