Lectures related to L-function

Characters and Dirichlet's Theorem

Introduces characters over a finite abelian group and explains the proof of the infinitude of primes in arithmetic progressions.

Primes in Arithmetic Progression

Explores primes in arithmetic progression, focusing on L-functions, characters, and the divergence of the sum of 1 over p for p congruent to a modulo q.

Functional Equation of Zeta

Covers the functional equation of zeta function and Jensen's formula in complex analysis.

Non-vanishing of Dirichlet L-function and Gamma functions

Covers the proof of non-vanishing of Quadratic Dirichlet L-function and reviews basic properties of Gamma function.

L-values and Extensions

Explores de Rham theory, L-values, and extensions, including special value formulas and examples related to Hecke characters and modular forms.

Algebraic Fields: Transcendence Degree

Explores transcendence degree in algebraic fields and classical analytic functions.

Dedekind Function: Analytic Continuation and Euler Product Formula

Covers the Dedekind function, Euler product formula, series convergence, and analytic continuation of logarithmic functions.