Zeta Functions Courses and Certifications

International Mathematical Union

The Distribution of Values of Zeta and L-Functions

Explore the intricate world of zeta and L-functions, delving into their value distribution patterns and mathematical implications with renowned number theorist Kannan Soundararajan.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

ICTP Mathematics

Modularity of Some Geometric Objects - Definitions, Reasons and State of the Art

Explore zeta functions, L-functions, and Galois representations in geometric objects, focusing on plane projective curves and their conjectured relationships with analytic functions.

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

Hausdorff Center for Mathematics

Spectral Gaps of Random Covers of Hyperbolic Surfaces

Explore spectral gaps in random hyperbolic surfaces, including Laplacian resonances and a probabilistic version of Selberg's 3/16 theorem, using transfer operators and zeta functions.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

James Maynard: Half-Isolated Zeros and Zero-Density Estimates

Innovative method for detecting zeta function zeros, improving classical zero density results and providing insights into prime number distribution in short intervals.

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

Insights into Mathematics

Infinite Series in 17th and 18th Century Mathematics

Explore the historical development of infinite series, from geometric series to complex exponentials, with insights into key mathematicians and groundbreaking formulas of the 17th and 18th centuries.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Frobenius Structure and p-adic Zeta Function

Explore p-adic Frobenius structures in differential equations, their connection to algebraic geometry, and their relation to p-adic zeta values in hypersurface families.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Fields Institute

Some Research Problems in Number Theory

Explore intriguing research problems in number theory with Ram Murty, delving into advanced mathematical concepts and unsolved questions in this fascinating field.

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

Fields Institute

Moments of Artin-Schreier L-functions

Explore the mathematical intricacies of Artin-Schreier L-functions and their moments in this advanced Fields Institute lecture by Matilde Lalín from Université de Montréal.

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

Insights into Mathematics

Euler's Product for the Zeta Function via Box Arithmetic - Part 2

Explores connections between Box Arithmetic and Number Theory, focusing on Euler's product formula for the Zeta function and its variants, including the sum of reciprocal squares of natural numbers.

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

Galileo Galilei Institute

Motivic Galois Theory of Algebraic Mellin Transforms

Explore the intricate connections between algebraic geometry and number theory through the lens of motivic Galois theory and Mellin transforms.

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

Galileo Galilei Institute

Scalar Modular Bootstrap and Zeros of the Zeta Function

Explore connections between modular bootstrap techniques and the Riemann zeta function's zeros, delving into mathematical physics and number theory.

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

Institut Henri Poincaré

Crystalline Measures and Zeta Functions

Explorez les liens entre mesures cristallines et fonctions zêta, en examinant leurs propriétés et relations avec la fonction zêta de Riemann. Une solution à une question ouverte est présentée.

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

Institut Henri Poincaré

Les fréquences de l'Univers

Explorez la formule reliant courbure géométrique et objets quantiques, et son interprétation récente dans le cadre de la relativité générale, établissant un lien entre théorie classique et monde quantique.

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

Institut des Hautes Etudes Scientifiques (IHES)

Fonctions sphéroïdales et triplets spectraux

Exploration des fonctions sphéroïdales et triplets spectraux pour reproduire les comportements des zéros de zêta, basée sur l'opérateur différentiel W et ses fonctions propres.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video