A. Akbary - On the distribution of the values of symmetric square L-functions in the half plane

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A. Akbary - On the distribution of the values of symmetric square L-functions in the half plane ${\rm Re}\,(s)>\frac{3}{2}$

A. AKBARY, Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada

On the distribution of the values of symmetric square L-functions in the half plane ${\rm Re}\,(s)>\frac{3}{2}$

Let L_sym²(f)(s) be the symmetric square L-function associated to a newform of weight 2 and level N. We will derive an asymptotic formula for the average values of L_sym²(f)(s) at a point s₀ in the half plane ${\rm Re}\,(s)> \frac{7}{4}$ . Assuming the Riemann hypothesis for the Riemann zeta function, we are able to extend our result to the half plane ${\rm Re}\,(s)>\frac{3}{2}$ .