On the Fourth Moment of Coefficients of Symmetric Square L-Function

Let f(z) be a holomorphic Hecke eigencuspform of weight k for the full modular group.Let λf(n) be the nth normalized Fourier coefficient of f(z).Suppose that L(sym2f,s) is the symmetric square L-function associated with f(z),and λsym2f(n) denotes the nth coefficient L(sym2f,s).In this paper,it is proved that where P2(t) is a polynomial in t of degree 2.Similarly,it is obtained that where ■2(t) is a polynomial in t of degree 2.

On the Distribution of Integral Ideals and Hecke Grssencharacters

The author uses analytic methods to study the distribution of integral ideals and Hecke Grssencharacters in algebraic number fields. Nowak’s results on the distribution of integral ideals, and Chandrasekharan and Good’s results on the distribution of Hecke Grssencharacters are improved.