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 to your own forgetting.

What you'll learn

30 lessons in Analytic Number Theory

Arithmetic functions & Dirichlet convolutionDirichlet convolution & Möbius inversionDirichlet seriesEuler productsThe Riemann zeta functionThe prime number theoremChebyshev's bounds & the ψ functionMertens' theoremsDirichlet characters & L-functionsThe Dirichlet hyperbola methodSieve methodsAbel summation & average ordersPrimes in arithmetic progressionsThe Riemann hypothesis & the error termLattice points & the circle problemPartitions & Hardy-RamanujanExponential sums & equidistributionBertrand's postulate & prime gapsThe functional equationCounting the zerosThe explicit formulaCharacter sumsSmooth numbersMean values of multiplicative functionsThe Erdos-Kac theoremBombieri-VinogradovBounded gaps between primesRamanujan's tau functionMoments of zetaRandom matrices and zeta
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 day its model predicts you would 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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