Dirichlet series

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Related lectures (31)

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Arithmetic functions

Covers the analysis of arithmetic functions, including prime numbers and the Riemann hypothesis.

Dirichlet Characters: Definition and Properties

Explores Dirichlet characters, covering their definition, periodicity, and properties through a mock exam.

Proof of Explicit Formula

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Modular Forms: Properties and Applications

Covers the properties and applications of modular forms and discusses equidistribution and modularity.

Vibration of Diatomic Molecules

Explores the vibration of diatomic AB molecules and Fourier series, emphasizing equations of motion and Dirichlet's theorem.

Dirichlet Series

Explores Dirichlet series convergence properties and absolute convergence conditions, with examples and applications.

Prime Gaps and Multiplicative Sieve Inequalities

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

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.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

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.