Asymptotics for the Dirichlet coefficients of symmetric power $L$-functions

On Artin’s L-functions. II: Dirichlet Coefficients

Critical Values of Symmetric Power L-functions

We consider the critical values of symmetric power L-functions attached to elliptic curves over Q. We show how to calculate a canonical Deligne period, and in several numerical examples, especially for sixth and tenth powers, we examine the factorisation of the rational number apparently obtained when one divides the critical value by the canonical period. This seems to provide some support for...

The Sixth Power Moment of Dirichlet L-functions

Understanding moments of families of L-functions has long been an important subject with many number theoretic applications. Quite often, the application is to bound the error term in an asymptotic expression of the average of an arithmetic function. Also, a good bound for a moments can be used to obtain a point-wise bound for an individual L-function in the family; strong enough bounds of this...

Spectral Asymptotics for Dirichlet Elliptic Operators with Non-smooth Coefficients

We consider a 2m-th-order elliptic operator of divergence form in a domain  of Rn, assuming that the coefficients are Hölder continuous of exponent r 2 (0, 1]. For the self-adjoint operator associated with the Dirichlet boundary condition we improve the asymptotic formula of the spectral function e( 2m , x , y) for x = y to obtain the remainder estimate O( n + dist(x , ) 1 n 1) with any 2 (0,...

Rectangular Symmetries for Coefficients of Symmetric Functions

We show that some of the main structural constants for symmetric functions (Littlewood-Richardson coefficients, Kronecker coefficients, plethysm coefficients, and the Kostka–Foulkes polynomials) share symmetries related to the operations of taking complements with respect to rectangles and adding rectangles.