In the field of nonlinear programming (in continuous variables) convex analysis [22, 23] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called " discrete convex analysis " [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid ...

The exposition here follows the lecture delivered at the summer school, and hence, contains neither precision, breadth of comprehension, nor depth of insight. The goal rather is the curious one of providing a loose introduction to the excellent introductions that already exist, together with scattered parenthetical commentary. The inadequate nature of the exposition is certainly worst in the th...

Abstract We study wide moments of Dirichlet L-functions using analytic properties the Lerch zeta function. Among other things we obtain an asymptotic expansion (with arbitrary twists) extending results Heath-Brown. also give applications to non-vanishing.