Monday 
Wednesday 
Friday 
Jan. 11
In Lecture:
 Jan. 13
In Lecture:
 Functorial properties of class field theory
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Jan. 15
In Lecture:

Jan. 18
In Lecture:
 No Class  Martin Luther King holiday
 Jan. 20
In Lecture:
 Applying class field theory to construct solvable extensions
 Ideles and Adeles
 Idele class groups
 Class field theory in the language of Ideles
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Jan. 22
In Lecture:
 Ideles and Adeles
 Idele class groups
 Class field theory in the language of Ideles
Associated Reading:
Video of class (streaming)
Video of class (downloadable)

Jan. 25
In Lecture:
 Comparing idele class groups with ray class groups
 The connected component of the identify of the idele classes
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Jan. 27
In Lecture:
 The idele class group of Q and of F_q(t)
 Leopold't conjecture
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Jan. 29
In Lecture:
 Global class field theory over function fields
Associated Reading:
Video of class (streaming)
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Feb. 1
In Lecture:
 Local class field theory (statments)
 Genus theory
Associated Reading:
Video of class (streaming)
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 Feb. 3
In Lecture:
 Genus theory, continued
 Ramification groups
Associated Reading:
Video of class (streaming)
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 Feb. 5
In Lecture:
 Ramification groups, continued
Associated Reading:
Video of class (streaming)
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Feb. 8
No class
 Feb. 10
No class
 Feb. 12
No class

Feb. 15
In Lecture:
Associated Reading:
 Samuel, chapter 2, sections 2.7, 2.8.
 Lang, chapter 3, section 3.3.
Video of class (streaming)
Video of class (downloadable)
 Feb. 17
In Lecture:
 Differents and lower ramification groups
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Feb. 19
In Lecture:
 Upper numbering of ramification groups
Associated Reading:
Video of class (streaming)
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Feb. 22
In Lecture:
 HasseArf Theorem
 Herbrand's Theorem
 Functorality of upper and lower numbering of the ramification groups
 Conductors, the Artin Representation
Associated Reading:
Video of class (streaming)
Video of class (downloadable)
 Feb. 24
In Lecture:
 Proof that the Artin character is the character of a representation
Associated Reading:
 Serre, Corps Locaux
 Lang, Algebraic number theory
Video of class (streaming)
Video of class (downloadable)
 Feb. 26
In Lecture:
 End of the proof that the Artin character is the character of a representation
 The Artin character and actions of finite groups on Jacobians
Associated Reading:
 Serre, Corps Locaux
 Lang, Algebraic number theory
Video of class (streaming)
Video of class (downloadable)

Mar. 1
In Lecture:
 The Artin character and actions of finite groups on Jacobians
 Artin Lfunctions
Associated Reading:
 Serre, Corps Locaux
 Lang, Algebraic number theory
Video of class (streaming)
Video of class (downloadable)
 Mar. 3
In Lecture:
 Abelian Lfunctions and Artin Lfunctions
Associated Reading:
 Lang, Algebraic number theory
Video of class (streaming)
Video of class (downloadable)
 Mar. 5
In Lecture:
 Functional equations of Artin Lfunctions
Associated Reading:
 Lang, Algebraic number theory
Video of class (streaming)
Video of class (downloadable)

Mar. 8
In Lecture:
 Mar. 10
In Lecture:
 Mar. 12
In Lecture:

Mar. 15
Rademacher Lecture by John Coates:
Video of the lecture (streaming)
Video of the lecture (downloadable)
 Mar. 16
Rademacher Lecture by John Coates:
 Cyclotomic Iwasawa theory
Video of the lecture (streaming)
Video of the lecture (downloadable)
 Mar. 17
Rademacher Lecture by John Coates:
 The general Main Conjecture
Video of the lecture (streaming)
Video of the lecture(downloadable)
Rademacher Lecture by John Coates:
 The TateShafarevich group and Iwasawa theory
Video of the lecture (streaming)
Video of the lecture(downloadable)

Mar. 22
In Lecture:
 Artin Lseries
 Relations between zeta and Lfunctions
Associated Reading:
 Lang, ``Algebraic Number theory," Chapter XII.
Video of class (streaming)
Video of class (downloadable)
 Mar. 24
In Lecture:
 The Burnside ring
 Zeta functions of curves over finite fields
Associated Reading:
 Mar. 26
In Lecture:
 Lfunctions of onedimensional representations over an imaginary quadratic fields
 Lfunctions of twodimensional Galois representations over Q and modular forms of weight 1
Associated Reading:
 Lang, Algebraic number theory
 G. Frey (editor), On Artin's conjecture for odd 2dimensional representations, Lecture notes in math. 1585 (1994), SpringerVerlag (available from gigapedia)
Video of class (streaming)
Video of class (downloadable)

Mar. 29
In Lecture:
 Zeta and Lfunctions over real quadratic fields
 Shintani formulas
Associated Reading:
 Lang, ``Algebraic Number theory."

Video of class (streaming)
Video of class (downloadable)
 Mar. 31
In Lecture:
 The Residue of the zeta functions of a number field at s = 1
Associated Reading:
 Lang, "Algebraic number theory," Chapters VI, VIII.
Video of class (streaming)
Video of class (downloadable)
 April 2
In Lecture:
 The Residue of the zeta functions of a number field at s = 1, continued
Associated Reading:
 Lang, "Algebraic number theory," Chapters VI, VIII.
Video of class (streaming)
Video of class (downloadable)

April 5
In Lecture:
 Functional equations of Lseries
 Leading terms in the Taylor expansions of Lseries at nonpositive integers
Associated Reading:
 Lang, ``Algebraic Number theory," Chapters XIII, XIV
 Washingon, L., "Introduction to cyclotomic fields," chapter 4. (Available on gigapedia)
 Ogg, Modular forms and Dirichlet series. (Available on gigapedia)
Video of class (streaming)
Video of class (downloadable)
 April 7
In Lecture:
 Functional equation of the Riemann zeta function (the classical proof)
 The functional equations of Artin Lfunctions
Associated Reading:
 Lang, "Algebraic number theory,"
 Ogg, "Modular forms and Dirichlet Series"
Video of class (streaming)
Video of class (downloadable)
 April 9
In Lecture:
 Leading term of the zeta function at s = 0
 Statement of Stark's conjecture
Associated Reading:
 Lang, Algebraic number theory
 Tate, Les conjectures de Stark sur les fonctions L en s = 0
Video of class (streaming)
Video of class (downloadable)

April 12
In Lecture:
 Computations of Stark regulators
Associated Reading:
 Lang, Algebraic number theory
 Tate, Les conjectures de Stark sur les fonctions L en s = 0
Video of class (streaming)
Video of class (downloadable)
 April 14
In Lecture:
 No class due to multiple oral exams!
 April 16
In Lecture:
 Constructing number fields using Stark's conjecture
Associated Reading:
 Lang, Algebraic number theory
 Tate, Les conjectures de Stark sur les fonctions L en s = 0
Video of class (streaming)
Video of class (downloadable)

April 19
In Lecture:
 The first order zero case of Stark's Conjecture (continued)
 Salem numbers and Stark's conjeccture
Associated Reading:
 Chinburg, T.: "Salem numbers and $L$functions."
J. Number Theory 18 (1984), no. 2, 213214.
 Tate, Les conjectures de Stark sur les fonctions L en s = 0
Video of class (streaming)
Video of class (downloadable)
 April 21
In Lecture:
 Salem numbers and Stark's Conjecture (continued)
Associated Reading:
 Chinburg, T.: "Salem numbers and $L$functions."
J. Number Theory 18 (1984), no. 2, 213214.
 Tate, Les conjectures de Stark sur les fonctions L en s = 0
Video of class (streaming)
Video of class (downloadable)
 April 23
In Lecture:
 Survey on Lehmer's Conjecture
 Lehmer's conjecture and closed geodesics on hyperbolic surfaces
Associated Reading:
 Ghate, Eknath; Hironaka, Eriko "The arithmetic and geometry of Salem numbers." Bull. Amer. Math. Soc. (N.S.) 38 (2001), no. 3, 293314
Video of class (streaming)
Video of class (downloadable)

April 26
In Lecture:
 Arithmetic hyperbolic surfaces and Salem numbers (continued)
 The Selberg trace formula and Weil's explicit formulas
Associated Reading:
 Sunada, Toshikazu, ``Riemannian coverings and isospectral manifolds."
Ann. of Math. (2) 121 (1985), no. 1, 169186.
 Lang, Algebraic number theory
Video of class (streaming)
Video of class (downloadable)
 April 28
In Lecture:
 April 30
In Lecture:
