This lecture sketches the proof of the Mordell Weil theorem, showing that the group of rational points on an elliptic curve or abelian variety is finitely generated.
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Mordell-Weil theorem
Selberg trace formula
Riemann mapping theorem
Vinberg lecture part 4. Automorphic forms
Vinberg lecture part 3. Kac-Moody algebras
Vinberg lecture part 2. The reflection group of II25,1
Vinberg lecture part 1.Vinberg's algorithm
Elliptic functions lecture 4. The sigma function
Borwein integrals
Elliptic functions lecture 3. Jacobi functions
Elliptic functions 1. Weierstrass function.
Introduction to number theory lecture 53. Three calculators for number theorists
Introduction to number theory lecture 52. Nonvanishing of L series at s=1.
Introduction to number theory lecture 51. Proof of Dirichlet's theorem
Introduction to number theory lecture 50. Dirichlet characters
Introduction to number theory lecture 49. Dirichlet's theorem
Introduction to number theory lecture 47. The prime number theorem
Introduction to number theory lecture 46. Products of Dirichlet series
Introduction to number theory lecture 45 Dirichlet series
Introduction to number theory lecture 44 Pythagorean triangles
Introduction to number theory lecture 43 Gaussian integers
Introduction to number theory lecture 42. Examples of indefinite binary quadratic forms.
Introduction to number theory lecture 41: More examples of binary quadratic forms
Introduction to number theory lecture 40. Examples of positive definite forms