Learning Path — Analytic Number Theory
Suggested preparation for Analytic Number Theory. Choose an entry point that fits your preparation.
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Entry / bridge route · Additional preparation for research reading · All paths
Entry / bridge route
Proofs & Mathematical Writing
Read quantified statements; write direct, contrapositive, contradiction and induction arguments.
Book of Proof — Richard Hammack. Direct open PDF
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You can explain the quantifiers in a statement and write these forms of proof without relying on a worked solution.
Elementary Number Theory
Use divisibility, congruences, Euclid’s algorithm and elementary reciprocity examples.
Elementary Number Theory: Primes, Congruences, and Secrets — William Stein. Direct open PDF
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You can prove elementary arithmetic statements and solve congruences, not just apply memorized formulas.
Calculus
Use limits, derivatives, integrals and series; distinguish computation from justification.
Calculus, Volume 1 — Gilbert Strang and Edwin 'Jed' Herman. Direct open PDF
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You can solve representative differentiation, integration and convergence exercises and explain the hypotheses used.
Real Analysis
Prove convergence, continuity, compactness and differentiation/integration results.
Basic Analysis I — Jiří Lebl. Direct open PDF
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You can work with epsilon arguments and prove standard compactness and convergence results, not just calculate limits.
Complex Analysis & Several Complex Variables
Study holomorphic functions, contour integration, series and residues.
Guide to Cultivating Complex Analysis: Working the Complex Field — Jiří Lebl. Direct open PDF
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You can apply Cauchy’s theorem and residue methods with hypotheses; several-variable material may require further preparation.
Analytic Number Theory
Combine arithmetic functions, asymptotic estimates and complex methods.
Notes on Analytic Number Theory — Kiran S. Kedlaya. Open online text / archive
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You can manipulate arithmetic functions and justify basic complex-analytic estimates; sieve methods need a separate bridge.
Research reading: additional tools
Choose according to the particular text, not as an obligation to complete every foundation again.