Langlands program and Ramanujan Conjecture: A survey

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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 p. 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 L-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.

Original languageEnglish
Title of host publicationMexican Mathematicians in the World Trends and Recent Contributions
EditorsFernando Galaz-García, Cecilia González-Tokman, Juan Carlos Pardo Millán
PublisherAmerican Mathematical Society
Pages161-204
Number of pages44
ISBN (Print)9781470465360
DOIs
StatePublished - 2021
Externally publishedYes
Event4th Meeting of Mexican Mathematicians Abroad, 2018 - Oaxaca, Mexico
Duration: 10 Jun 201815 Jun 2018

Publication series

NameContemporary Mathematics
Volume775
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

Conference4th Meeting of Mexican Mathematicians Abroad, 2018
Country/TerritoryMexico
CityOaxaca
Period10/06/1815/06/18

Keywords

  • L-functions
  • Langlands Program
  • Ramanujan Conjecture

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