Introduction to Analytic Number Theory"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS |
Contents
Historical Introduction | 1 |
The Fundamental Theorem of Arithmetic | 13 |
Chapter | 14 |
Chapter 2 | 24 |
7 | 30 |
Chapter 3 | 52 |
Chapter 4 | 74 |
Chapter 5 | 106 |
Periodic Arithmetical Functions and Gauss Sums | 157 |
Chapter 9 | 177 |
Primitive Roots | 204 |
Chapter 11 | 223 |
9 | 238 |
Chapter 12 | 249 |
Chapter 13 | 278 |
Partitions | 304 |
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Common terms and phrases
a₁ absolute convergence analytic arithmetical function Assume asymptotic formula Bell series coefficients common divisor completely multiplicative completes the proof converges absolutely deduce defined Dirichlet character mod Dirichlet characters Dirichlet series Dirichlet's theorem divides elements example Exercises for Chapter exists finite functional equation ƒ and g Gauss sums given half-plane Hence identity implies induced modulus inequality infinitely many primes integers lattice points Lemma Let G linear congruence log log log² m₁ Möbius function mod p² modulo multiplicative function nonresidue Note O(log obtain odd prime P₁ partial sums positive integers prime factors prime number theorem primitive mod primitive root mod principal character properties quadratic nonresidue quadratic reciprocity law quadratic residues r₁ reduced residue system relation relatively prime residue classes residue system mod Riemann zeta function satisfies subgroup term theory write X₁ Σ Σ