Author | Hlawka, Edmund. author |
---|---|
Title | Geometric and Analytic Number Theory [electronic resource] / by Edmund Hlawka, Rudolf Taschner, Johannes Schoiร{159}engeier |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1991 |
Connect to | http://dx.doi.org/10.1007/978-3-642-75306-0 |
Descript | X, 238p. 15 illus. online resource |
1. The Dirichlet Approximation Theorem -- Dirichlet approximation theorem โ{128}{148} Elementary number theory โ{128}{148} Pell equation โ{128}{148} Cantor series โ{128}{148} Irrationality of ?(2) and ?(3) โ{128}{148} multidimensional diophantine approximation โ{128}{148} Siegelโ{128}{153}s lemma โ{128}{148} Exercises on Chapter 1. -- 2. The Kronecker Approximation Theorem -- Reduction modulo 1 โ{128}{148} Comments on Kroneckerโ{128}{153}s theorem โ{128}{148} Linearly independent numbers โ{128}{148} Estermannโ{128}{153}s proof โ{128}{148} Uniform Distribution modulo 1 โ{128}{148} Weylโ{128}{153}s criterion โ{128}{148} Fundamental equation of van der Corput โ{128}{148} Main theorem of uniform distribution theory โ{128}{148} Exercises on Chapter 2. -- 3. Geometry of Numbers -- Lattices โ{128}{148} Lattice constants โ{128}{148} Figure lattices โ{128}{148} Fundamental region โ{128}{148} Minkowskiโ{128}{153}s lattice point theorem โ{128}{148} Minkowskiโ{128}{153}s linear form theorem โ{128}{148} Product theorem for homogeneous linear forms โ{128}{148} Applications to diophantine approximation โ{128}{148} Lagrangeโ{128}{153}s theorem โ{128}{148} the lattice?(i) โ{128}{148} Sums of two squares โ{128}{148} Blichfeldtโ{128}{153}s theorem โ{128}{148} Minkowskiโ{128}{153}s and Hlawkaโ{128}{153}s theorem โ{128}{148} Rogersโ{128}{153} proof โ{128}{148} Exercises on Chapter 3. -- 4. Number Theoretic Functions -- Landau symbols โ{128}{148} Estimates of number theoretic functions โ{128}{148} Abel transformation โ{128}{148} Eulerโ{128}{153}s sum formula โ{128}{148} Dirichlet divisor problem โ{128}{148} Gauss circle problem โ{128}{148} Square-free and k-free numbers โ{128}{148} Vinogradovโ{128}{153}s lemma โ{128}{148} Formal Dirichlet series โ{128}{148} Mangoldtโ{128}{153}s function โ{128}{148} Convergence of Dirichlet series โ{128}{148} Convergence abscissa โ{128}{148} Analytic continuation of the zeta- function โ{128}{148} Landauโ{128}{153}s theorem โ{128}{148} Exercises on Chapter 4. -- 5. The Prime Number Theorem -- Elementary estimates โ{128}{148} Chebyshevโ{128}{153}s theorem โ{128}{148} Mertensโ{128}{153} theorem โ{128}{148} Eulerโ{128}{153}s proof of the infinity of prime numbers โ{128}{148} Tauberian theorem of Ingham and Newman โ{128}{148} Simplified version of the Wiener-Ikehara theorem โ{128}{148} Mertensโ{128}{153} trick โ{128}{148} Prime number theorem โ{128}{148} The ?-function for number theory in ?(i) โ{128}{148} Heckeโ{128}{153}s prime number theorem for ?(i) โ{128}{148} Exercises on Chapter 5. -- 6. Characters of Groups of Residues -- Structure of finite abelian groups โ{128}{148} The character group โ{128}{148} Dirichlet characters โ{128}{148} Dirichlet L-series โ{128}{148} Prime number theorem for arithmetic progressions โ{128}{148} Gauss sums โ{128}{148} Primitive characters โ{128}{148} Theorem of Pรณlya and Vinogradov โ{128}{148} Number of power residues โ{128}{148} Estimate of the smallest primitive root โ{128}{148} Quadratic reciprocity theorem โ{128}{148} Quadratic Gauss sums โ{128}{148} Sign of a Gauss sum โ{128}{148} Exercises on Chapter 6. -- 7. The Algorithm of Lenstra, Lenstra and Lovรกsz -- Addenda -- Solutions for the Exercises -- Index of Names -- Index of Terms