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Representation Theory and Automorphic Forms pp 151–173Cite as

Langlands Functoriality Conjecture and Number Theory

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Part of the book series: Progress in Mathematics ((PM,volume 255))

Summary

We discuss several applications of the recent developments in the Langlands functoriality conjecture such as the automorphy of the symmetric powers of 2-dimensional complex representations of Galois groups of number fields, lattice point problems, Ramanujan– Selberg and Sato–Tate conjectures.We conclude by explaining how these recent developments are established.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, Indiana

    Freydoon Shahidi

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  1. Freydoon Shahidi
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Editors and Affiliations

  1. RIMS, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

    Toshiyuki Kobayashi

  2. Department of Mathematics, Harvard University, Cambridge, MA 02138, U.S.A

    Wilfried Schmid

  3. Department of Mathematics, Inha University, Incheon 402-751, Republic of Korea

    Jae-Hyun Yang

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Shahidi, F. (2008). Langlands Functoriality Conjecture and Number Theory. In: Kobayashi, T., Schmid, W., Yang, JH. (eds) Representation Theory and Automorphic Forms. Progress in Mathematics, vol 255. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4646-2_5

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