negative one. This can be seen graphically as a "kink" or a "cusp" in the graph at x = 0. Even a function with a smooth graph is not differentiable at a point where its tangent is vertical: For instance, the function y = x1/3 is not differentiable at x = 0. ...
Let f be a fixed self-dual Hecke-Maass cusp form for SL(3, Z) and {mu(j)} be an orthogonal basis of odd Hecke-Maass cusp forms for SL(2, Z). We prove an asymptotic formula for the average of the first derivative of the Rankin-Selberg L-function of f and mu(j) at the ...
If you were thinking that theme code is a separate work because it is contained in a separate file, also consider that many core WordPress files work the same way. They define functions, they use the WordPress hook system to insert themselves at various places in the code, they perform ...
We show that a positive proportion of the derivatives of L-functions associated to holomorphic cusp forms of large weight do not vanish at the central point. Specifically, by optimizing the choice of quadratic form in the mollified moments of the L-function, we prove that this proportion is ...