Factoring $L$-functions as products of $L$-functions

Kernels for products of L-functions

The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their nonholomorphic analogs and show their connection to values of L-functions outside the critical strip.

L-Functions for Symmetric Products of Kloosterman Sums

The classical Kloosterman sums give rise to a Galois representation of the function field unramfied outside 0 and ∞. We study the local monodromy of this representation at ∞ using l-adic method based on the work of Deligne and Katz. As an application, we determine the degrees and the bad factors of the L-functions of the symmetric products of the above representation. Our results generalize som...

L-convex Functions and M-convex Functions

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 ...

Monoids and L-functions

Motives : Motivic L - functions

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...