In this memoir we study the local theory for Rankin Selberg convolutions for the degree 2ℓn standard [italic]L-function of generic representations of [italic]SO[subscript]2ℓ+1 ([italic capital]F) x GL[subscript italic]n ([italic capital]G) over a local field [italic capital]F.
In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form.…
Introduction Local cohomology groups Global cohomology groups and Selmer structures Kolyvagin systems Kolyvagin systems over principal artinian rings Kolyvagin systems over integral domains Examples Appendix A. Proof of Theorem 3.2.4 Appendix B. Proof of Theorem 4.3.3, by Benjam…
Arithmetic of L-functions
by Rubin, Karl, Popescu, Cristian, Silverberg, Alice
fromIAS/Park City mathematics series
"Traditionally, p-adic L-functions have been constructed from complex L-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of p-adic L-functions coming directly from p-adic Galois representations (or, more generally, from motives). Thi…
Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the t…