TY - GEN
T1 - Langlands program and Ramanujan Conjecture
T2 - 4th Meeting of Mexican Mathematicians Abroad, 2018
AU - Lomelí, Luis Alberto
N1 - Publisher Copyright:
© 2021 American Mathematical Society.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - L-functions
KW - Langlands Program
KW - Ramanujan Conjecture
UR - http://www.scopus.com/inward/record.url?scp=85124123619&partnerID=8YFLogxK
U2 - 10.1090/conm/775/15592
DO - 10.1090/conm/775/15592
M3 - Conference contribution
AN - SCOPUS:85124123619
SN - 9781470465360
T3 - Contemporary Mathematics
SP - 161
EP - 204
BT - Mexican Mathematicians in the World Trends and Recent Contributions
A2 - Galaz-García, Fernando
A2 - González-Tokman, Cecilia
A2 - Pardo Millán, Juan Carlos
PB - American Mathematical Society
Y2 - 10 June 2018 through 15 June 2018
ER -