Second Moment of the GL_3 Standard L-function on the Critical Line
Explore advanced number theory concepts, focusing on GL_3 L-functions, moments of the Riemann zeta function, and applications to the Rankin-Selberg problem.
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.
Time and Band Limiting for Exceptional Orthogonal Polynomials
Explore time-and-band limiting in exceptional orthogonal polynomials, connecting integral operators, differential equations, and bispectral problems. Uncover links to KdV equations and random matrix theory.
What Is the Riemann Hypothesis?
Explore the Riemann Hypothesis, convergent series, and Euler's solutions in this engaging introduction to complex mathematical concepts and their implications.
The Big Mathematics Divide - Between "Exact" and "Approximate" - Sociology and Pure Maths
Explores the divide between exact and approximate theories in pure mathematics, challenging conventional views on arithmetic, algebra, topology, and number theory, including the Riemann Hypothesis.
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.
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.
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.
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.
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.
A Construction of Apéry Constants from Landau Ginzberg Models
Explores construction of Apéry constants from Landau-Ginzberg models, linking quantum differential equations of Fano threefolds to mirror symmetry and geometric higher normal functions.
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.
Primes, Postdocs and Pretentiousness - 2021 CRM-Fields-PIMS Prize Lecture
Explore prime numbers, academic careers, and mathematical concepts in this engaging lecture by renowned mathematician Andrew Granville, offering insights into number theory and research.
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.
Euler's Product for the Zeta Function via Box Arithmetic - Part 1
Explore box arithmetic's application to number theory, focusing on the Euler product for the Riemann zeta function and the Fundamental Identity of Arithmetic in a combinatorial framework.
Multiplicative Functions and Dirichlet Series via Boxes - Part 2
Explores Dirichlet series and box arithmetic, offering a novel approach to number theory concepts without relying on infinity. Introduces caretation and algebraic structures for encoding Dirichlet series.
Euler Product Formula - A Beautiful Equation in Number Theory
Discover the beauty of the Euler Product Formula, connecting sums over natural numbers to products over primes. Explore its proof, applications, and links to the Riemann Hypothesis.
Subconvexity of L-functions - Part 3
Explore advanced concepts in subconvexity of L-functions with mathematician Paul Nelson in this in-depth conference talk from the "Building bridges 6th EU/US" meeting.
Subconvexity of L-functions - Part 1
Explore advanced concepts in analytic number theory, focusing on subconvexity bounds for L-functions and their applications in mathematics.
Subconvexity of L-functions - Part 4
Explore advanced concepts in subconvexity of L-functions with mathematician Paul Nelson in this in-depth conference talk from the "Building bridges 6th EU/US" meeting.
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.