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Analytic number theory is a category of mathematical books focused on studying integers—especially prime numbers—using tools from analysis, such as complex analysis and Fourier/harmonic analysis. Typical topics include the distribution of primes (e.g., the Prime Number Theorem), zeta and L-functions (like the Riemann zeta function and Dirichlet L-functions), sieve methods, exponential sums, modular and automorphic forms, and additive problems such as Goldbach’s and Waring’s conjectures. Books in this genre emphasize asymptotic formulas, bounds, and rigorous analytic techniques including contour integration, Dirichlet series, Tauberian theorems, and explicit estimates. The category spans introductory graduate texts, advanced monographs, research treatises, and problem collections, often connecting to algebraic number theory, combinatorics, and representation theory, with occasional applications to cryptography and randomness.

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