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Analytic Number Theory

by Donald J. Newman · Donald J. Newman

Springer graduate text (GTM 177) presenting analytic number theory through selected problems: the partition function, the Erdős–Fuchs theorem, Waring's problem, nonvanishing of L-series, and Newman's short proof of the prime number theorem. Readers see how complex analysis and generating functions solve counting questions.

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But what is the Riemann zeta function? Visualizing analytic continuation

Animated 3Blue1Brown explanation of how the zeta function is defined for complex inputs and extended beyond its region of convergence by analytic continuation. Viewers come to understand what the Riemann hypothesis actually claims and why it connects to the primes.

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MathOverflow Analytic Number Theory

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Terence Tao's Blog

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Introduction to Analytic Number Theory

Classic undergraduate text on analytic number theory, covering arithmetical functions, Dirichlet multiplication, averages, the distribution of primes, Dirichlet's theorem on primes in progressions, Dirichlet series, and the Riemann zeta function. Readers learn the core analytic methods behind the prime number theorem.

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