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arXiv · 1812.05203

Langlands Program and Ramanujan Conjecture: a survey

Luis Alberto Lomelí
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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.

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Luis Alberto Lomelí. 2018-12-13. Langlands Program and Ramanujan Conjecture: a survey. https://arxiv.org/abs/1812.05203

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