Modular Forms and L-functions

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See also [vignettes], [representation theory], [alg number theory], [functional analysis], [Lie theory], [algebra], [complex analysis]. (2005-06 notes and 2010-11 notes lower on the page)

Math 8207-08, 2013-14, (Spring: 206 Vincent Hall) 11:15-12:05, MWF

This course introduces many phenomena that led to much contemporary research, including the Langlands program and much more. Little prior acquaintance with higher-level prerequisites is assumed. Rather, we will give examples that led to formation of many contemporary concepts and abstractions in number theory, complex analysis, Lie theory, harmonic analysis, representation theory, and algebraic geometry.

Units are listed in reverse chronological order. Notes will be linked-to as we go, somewhat in advance of progress in-class. If you must print notes, please don't do so until just before reading, because many updates will occur.

See also Number theory notes 2011-12 for related discussions

Our course will include much supporting material, beyond the strict topics of the title. Samples of other sources about modular forms themselves are below. Siegel's notes give number-theoretic applications of Hilbert modular forms.

Math 8207-08, 2010-11, 209 Vincent Hall, 2:30-3:20, MWF

Office hours: MWF 1:25-2:15 or by appointment, email anytime

An introduction to number theory, zeta functions and L-functions, and the role of modular and automorphic forms

Notes and exercises (reverse chrono order)

Notes from 2005-06

Notes (reverse chronological order):
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