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Notes on analytic number theory [Kedlaya] - mklabgr - 07-09-2026
Notes on analytic number theory
BY Kiran S. Kedlaya
Summary
Notes on Analytic Number Theory provides a comprehensive introduction to one of the most influential branches of modern mathematics, exploring how analytic techniques can be used to understand the behavior of integers and, above all, the distribution of prime numbers. Beginning with the fundamental relationship between the additive and multiplicative properties of integers, the text develops the essential tools of analytic number theory, including Dirichlet series, Euler products, the Riemann zeta function, and Dirichlet L-functions.
These concepts are used to establish major results such as the Prime Number Theorem, Dirichlet’s theorem on primes in arithmetic progressions, and increasingly refined estimates for the distribution of primes, while also introducing the role of the Riemann Hypothesis and related conjectures in understanding error terms and the behavior of zeta-function zeroes.
BOOK