Prime Distribution
Prime number theorem, sieve methods, and gaps between primes.
Prime Distribution. Prime number theorem, sieve methods, and gaps between primes.
Foundations and canonical references
The standard treatments of prime distribution approach the subject from complementary angles. Davenport, Multiplicative Number Theory (2000) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Mazur, Prime Numbers and the Riemann Hypothesis (2016) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for prime distribution include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2000Multiplicative Number Theorydavenport-2000
- textbook · supporting · 2016Prime Numbers and the Riemann Hypothesismazur-2016, stein-2016
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