Riemann Zeta Function Courses and Certifications

Michael Penn

Another Riemann-Zeta Function Identity

Explore an intriguing identity involving even values of the Riemann-Zeta function, delving into limits, sums, and transformations to uncover mathematical insights.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Michael Penn

More Identities Involving the Riemann-Zeta Function

Explore combinatorial techniques to derive new identities for the Riemann-Zeta function, building on previous mathematical concepts and expanding analytical understanding.

• YouTube
• 23 minutes
• On-Demand
• Free Video

Michael Penn

Some Identities Involving the Riemann-Zeta Function

Explore the Riemann-Zeta function, its generating function for positive even integers, and derive sum identities in this mathematical deep dive.

• YouTube
• 26 minutes
• On-Demand
• Free Video

ICTP Mathematics

On the Riemann Zeta-Function, Fourier Optimization and Quadratic Forms

Explore the Riemann zeta-function, Fourier analysis, and quadratic forms in number theory. Delve into Selberg's theorem, Berry's conjecture, and representation of integers by quadratic forms.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Fields Institute

The Eighth and Shifted Moments of the Riemann Zeta Function

Explore advanced mathematical concepts related to the Riemann zeta function, focusing on its eighth and shifted moments in this specialized lecture by Peng-Jie Wong.

• YouTube
• 34 minutes
• On-Demand
• Free Video

Mathologer

Ramanujan - Making Sense of 1+2+3+... = -1/12 and Co.

Explore the mathematical paradox of infinite sums equaling unexpected values, delving into Ramanujan's work, summation rules, and connections to the Riemann Zeta function.

• YouTube
• 35 minutes
• On-Demand
• Free Video

Physics Explained

The 15-Year-Old Who Discovered the Law of Primes

Explore the fascinating journey from Euclid's proof to Gauss's teenage discovery of prime distribution, uncovering how mathematical chaos yields elegant laws.

• YouTube
• 47 minutes
• On-Demand
• Free Video

3Blue1Brown

Visualizing the Riemann Zeta Function and Analytic Continuation

Explore the Riemann zeta function's visualization, analytic continuation, and its connection to the famous Riemann hypothesis through engaging animations and clear explanations.

• YouTube
• 22 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

The Finite Part of Infinity by Joseph Samuel

Explore the paradoxical equation 1+2+3...=-1/12, its mathematical interpretation, and its impact on physics, including the Casimir effect, with insights from differential geometry and topology.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Michael Penn

A Very Riemann-Zeta Sum

Explore advanced mathematical techniques for evaluating complex sums related to the Riemann zeta function through detailed problem-solving methods.

• YouTube
• 14 minutes
• On-Demand
• Free Video

Wolfram

Zeta Functions - From Riemann to Feynman

Explore zeta functions from Riemann to Feynman, covering harmonic numbers, polylogarithms, and their applications in number theory, combinatorics, and Feynman integrals with Wolfram tools.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Wrath of Math

Euler's Proof of the Infinitude of Primes Using the Riemann Zeta Function

Discover Euler's elegant approach to proving infinite primes through the Riemann Zeta function, exploring a sophisticated alternative to Euclid's classical contradiction method.

• YouTube
• 18 minutes
• On-Demand
• Free Video

University of Chicago Department of Mathematics

Bounds on the Density of Zeroes of the Riemann Zeta Function in Strips

Explore Larry Guth's research on bounds of Riemann zeta function zeroes, their relation to prime distribution, and recent findings with Maynard in this mathematical symposium talk.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Simons Foundation

Joint Moments of Characteristic Polynomials and the Riemann Zeta-Function

Explore joint moments of characteristic polynomials in random unitary matrices and their connection to Riemann zeta-function derivatives on the critical line.

• YouTube
• 1 hour
• On-Demand
• Free Video

Simons Foundation

The Square of the Riemann Zeta Function Gives Rise to Critical Multiplicative Chaos

Explore the connection between the Riemann zeta function's square and critical multiplicative chaos, revealing deep links between random measures and number theory through recent conjecture proofs.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video