Analytic number theory

Related lectures (24)

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Covers the definition of generating functions and their application in solving recurrence relations.

Counting with Recurrence Relations: Summary

Explores counting with recurrence relations, linear recurrence relations, generating functions, and counting principles.

Advanced Counting: Generating Functions and Recurrence Relations

Explores generating functions, recurrence relations, and advanced counting techniques.

Convergence and Divergence of Series

Covers the definitions of convergent and divergent series and explores the harmonic series and alternating series.

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Binomial Coefficients: Estimation and Stirling's Formula

Explores binomial coefficient estimation, Stirling's formula, and properties of the bell curve.

Sequences: Arithmetic and Geometric Progressions

Covers arithmetic and geometric progressions, strings, and recurrence relations.

Sequences: Relations, Summation, Strings

Covers arithmetic and geometric progressions, strings, and recurrence relations in sequences.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Linear Recurrence Relations: Solving Techniques and Examples

Explains linear homogeneous recurrence relations and provides solving techniques and examples.

Recursive Sequences: Convergence and Limits

Covers the study of recursive sequences, focusing on convergence and limits.

Smooth Dynamics: Bernoulli and K Properties

Explores Bernoulli and K properties in smooth dynamics, including equivalence, examples, and implications.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Stirling's Formula and Functional Equation for Zeta Log in to Mediaspace to watch this video

Covers the proof of Stirling's asymptotic formula for the Gamma function and the functional equation of the Zeta function.

Functional Equation of Zeta and Hadamard Products Log in to Mediaspace to watch this video

Covers the functional equation of the Zeta function and the Hadamard factorization theorem.

Convergence of Series Log in to Mediaspace to watch this video

Explores the convergence criteria of numerical series, including absolute convergence and alternating series.

Convergence of Series Log in to Mediaspace to watch this video

Explores point of accumulation, Bolzano-Weierstrass theorem, and series convergence, including harmonic series examples.

Maximum Principle in Harmonic Functions Log in to Mediaspace to watch this video

Explores the maximum principle in harmonic functions and its implications for uniqueness and bounds on solutions.

Polynomials: Theory and Applications Log in to Mediaspace to watch this video

Covers the theory of polynomials, including definitions, properties, and applications.