Elementary theory of L-functions and modular forms

Syllabus

The Riemann zeta function

• Euler and the zeta function LN: 1, 2.
• On Riemann's memoir LN: 3, 4.
• Newman's short proof of the PNT LN: 5, 6, 7.
• On Jacobi's theta function LN: 8, 9.

Dirichlet L-series

• Characters of finite abelian groups LN: 10, 11.
• Dirichlet series and L-functions LN: 12, 13.
• Dirichlet's theorem LN: 14.
• On Chebotarev's density theorem LN: 15, 16.

Further L-functions and reciprocity

• On the class number LN: 17, 18.
• Dirichlet's class number formula LN: 19, 20.
• Revisiting quadratic reciprocity LN: 21, 22.
• On the Hasse-Weil L-function LN: 23, 24.

Modular forms

• Basic notions LN: 25, 26.
• Dimension formula LN: 27, 28.
• Hecke operators LN: 29 - 30.
• Theta functions LN: 31, 32.

Facultad de Ciencias
Bernal Diaz del Castillo 340
28045 Colima
Mexico