Introduction to Analytic Number Theory
Springer Berlin (Verlag)
978-3-642-46126-2 (ISBN)
I The unique factorization theorem.-
1. Primes.-
2. The unique factorization theorem.-
3. A second proof of Theorem 2.-
4. Greatest common divisor and least common multiple.-
5. Farey sequences.-
6. The infinitude of primes.- II Congruences.-
1. Residue classes.-
2. Theorems of Euler and of Fermat.-
3. The number of solutions of a congruence.- III Rational approximation of irrationals and Hurwitz's theorem.-
1. Approximation of irrationals.-
2. Sums of two squares.-
3. Primes of the form 4k±.-
4. Hurwitz's theorem.- IV Quadratic residues and the representation of a number as a sum of four squares.-
1. The Legendre symbol.-
2. Wilson's theorem and Euler's criterion.-
3. Sums of two squares.-
4. Sums of four squares.- V The law of quadratic reciprocity.-
1. Quadratic reciprocity.-
2. Reciprocity for generalized Gaussian sums.-
3. Proof of quadratic reciprocity.-
4. Some applications.- VI Arithmetical functions and lattice points.-
1. Generalities.-
2. The lattice point function r(n).-
3. The divisor function d(n).-
4. The functions ?(n).-
5. The Möbius functions ?(n).-
6. Euler's function ?(n).- VII Chebyshev's therorem on the distribution of prime numbers.-
1. The Chebyshev functions.-
2. Chebyshev's theorem.-
3. Bertrand's postulate.-
4. Euler's identity.-
5. Some formulae of Mertens.- VIII Weyl's theorems on uniforms distribution and Kronecker's theorem.-
1. Introduction.-
2. Uniform distribution in the unit interval.-
3. Uniform distribution modulo 1.-
4. Weyl's theorems.-
5. Kronecker's theorem.- IX Minkowski's theorem on lattice points in convex sets.-
1. Convex sets.-
2. Minkowski's theorem.-
3. Applications.- XDirichlet's theorem on primes in an arithmetical progression.-
1. Introduction.-
2. Characters.-
3. Sums of characters, orthogonality relations.-
4. Dirichlet series, Landau's theorem.-
5. Dirichlet's theorem.- XI The prime number theorem.-
1. The non-vanishing of ? (1 + it).-
2. The Wiener-Ikehara theorem.-
3. The prime number theorem.- A list of books.- Notes.
Erscheint lt. Verlag | 1.3.2012 |
---|---|
Reihe/Serie | Grundlehren der mathematischen Wissenschaften |
Zusatzinfo | VIII, 144 p. |
Verlagsort | Berlin |
Sprache | englisch |
Maße | 155 x 235 mm |
Gewicht | 241 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
Schlagworte | Analytic number theory • Analytische Zahlentheorie • arithmetic • Boundary element method • Number Theory • Prime number • Proof • Time |
ISBN-10 | 3-642-46126-3 / 3642461263 |
ISBN-13 | 978-3-642-46126-2 / 9783642461262 |
Zustand | Neuware |
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