Discrete Mathematics

Learn Analytic Number Theory

Primes through the lens of analysis: Dirichlet series and Euler products, the Riemann zeta function, the prime number theorem, Chebyshev bounds, Mertens' theorems, L-functions, sieves, and summation techniques.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

10 lessons in Analytic Number Theory

Arithmetic functions & Dirichlet convolutionDirichlet series & Euler productsThe Riemann zeta functionThe prime number theoremChebyshev's bounds & the ψ functionMertens' theoremsDirichlet characters & L-functionsThe Dirichlet hyperbola methodSieve methodsAbel summation & average orders
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the moment just before you'd forget it. A short placement check finds what you already know, so you start Analytic Number Theory exactly where it's useful.

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