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This is an introduction to analytic number theory developed through the study of the distribution of prime numbers, highlighting how analytic number theorists think. The central focus is on the Prime Number Theorem, presented through a proof selected to balance conceptual understanding with technical depth, alongside a sketch of Riemann's classical approach to highlight the subject's elegance. Providing a wide range of further directions (e.g., sieve methods, the anatomy of integers, primes in arithmetic progressions, prime gaps, smooth numbers, and extensive discussion of probabilistic...

Number Theory Revealed: An Introduction acquaints undergraduates with the ""Queen of Mathematics"". The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms and large solutions of equations. Each chapter includes an ""elective appendix"" with...

From July 11th to July 22nd, 2005, a NATO advanced study institute, as part of the series Seminaire de mathematiques superieures, was held at the U- versite de Montreal, on the subject Equidistribution in the theory of numbers. There were about one hundred participants from sixteen countries around the world. This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have...

From July 11th to July 22nd, 2005, a NATO advanced study institute, as part of the series Seminaire de mathematiques superieures, was held at the U- versite de Montreal, on the subject Equidistribution in the theory of numbers. There were about one hundred participants from sixteen countries around the world. This volume presents details of the lecture series that were given at the school. Across the broad panorama of topics that constitute modern number t- ory one nds shifts of attention and focus as more is understood and better questions are formulated. Over the last decade or so we have...

Number Theory Revealed: A Masterclass acquaints enthusiastic students with the ""Queen of Mathematics''. The text offers a fresh take on congruences, power residues, quadratic residues, primes, and Diophantine equations and presents hot topics like cryptography, factoring, and primality testing. Students are also introduced to beautiful enlightening questions like the structure of Pascal's triangle mod $p$ and modern twists on traditional questions like the values represented by binary quadratic forms, the anatomy of integers, and elliptic curves. This Masterclass edition contains many...