Langlands Program and Ramanujan Conjecture: a survey
Number Theory
2018-12-14 v1
Abstract
We present topics in the Langlands Program to graduate students and a wider mathematically mature audience. We study both global and local aspects in characteristic zero as well as characteristic . We look at modern approaches to the generalized Ramanujan conjecture, which is an open problem over number fields, and present known cases over function fields. In particular, we study automorphic -functions via the Langlands-Shahidi method. Hopefully, our approach to the Langlands Program can help guide the interested reader into an exciting field of mathematical research.
Cite
@article{arxiv.1812.05203,
title = {Langlands Program and Ramanujan Conjecture: a survey},
author = {Luis Alberto Lomelí},
journal= {arXiv preprint arXiv:1812.05203},
year = {2018}
}