Geometric and analytic number theory:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1991
|
| Schriftenreihe: | Universitext
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002842528&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 205 - 207 |
| Umfang: | X, 238 S. graph. Darst. |
| ISBN: | 9783540520160 3540520163 0387520163 |
Internformat
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| 240 | 1 | 0 | |a Geometrische und analytische Zahlentheorie |
| 245 | 1 | 0 | |a Geometric and analytic number theory |c Edmund Hlawka ; Johannes Schoissengeier ; Rudolf Taschner |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1991 | |
| 300 | |a X, 238 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1819300182978723840 |
|---|---|
| adam_text | Contents
1. The Dirichlet Approximation Theorem 1
Dirichlet approximation theorem Elementary number theory Pell equa¬
tion Cantor series Irrationality of £(2) and £(3) multidimensional
diophantine approximation Siegel s lemma Exercises on Chapter 1.
2. The Kronecker Approximation Theorem 19
Reduction modulo 1 Comments on Kronecker s theorem Linearly in¬
dependent numbers Estermann s proof Uniform Distribution modulo
1 Weyl s criterion Fundamental equation of van der Corput Main
theorem of uniform distribution theory Exercises on Chapter 2.
3. Geometry of Numbers 38
Lattices Lattice constants Figure lattices Fundamental region
Minkowski s lattice point theorem Minkowski s linear form theorem
Product theorem for homogeneous linear forms Applications to diophan¬
tine approximation Lagrange s theorem the lattice TL(i) Sums of
two squares Blichfeldt s theorem Minkowski s and Hlawka s theorem
Rogers proof Exercises on Chapter 3.
4. Number Theoretic Functions 71
Landau symbols Estimates of number theoretic functions Abel trans¬
formation Euler s sum formula Dirichlet divisor problem Gauss circle
problem Square free and fc free numbers Vinogradov s lemma Formal
Dirichlet series Mangoldt s function Convergence of Dirichlet series
Convergence abscissa Analytic continuation of the zeta function Lan¬
dau s theorem Exercises on Chapter 4.
5. The Prime Number Theorem 106
Elementary estimates Chebyshev s theorem Mertens theorem Euler s
proof of the infinity of prime numbers Tauberian theorem of Ingham and
Newman Simplified version of the Wiener Ikehara theorem Mertens
trick Prime number theorem The ^ function for number theory in Z(i)
Hecke s prime number theorem for Z(t) Exercises on Chapter 5.
X Contents
6. Characters of Groups of Residues 138
Structure of finite abelian groups The character group Dirichlet char¬
acters Dirichlet L series Prime number theorem for arithmetic pro¬
gressions Gauss sums Primitive characters Theorem of Polya and
Vinogradov Number of power residues Estimate of the smallest primi¬
tive root Quadratic reciprocity theorem Quadratic Gauss sums Sign
of a Gauss sum Exercises on Chapter 6.
7. The Algorithm of Lenstra, Lenstra and Lovasz 173
Addenda 184
Bibliography 205
Solutions for the Exercises 208
Index of Names 235
Index of Terms 237
|
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| author | Hlawka, Edmund 1916-2009 Schoißengeier, Johannes 1948- Taschner, Rudolf 1953- |
| author_GND | (DE-588)118810065 (DE-588)138375534 (DE-588)130153222 |
| author_facet | Hlawka, Edmund 1916-2009 Schoißengeier, Johannes 1948- Taschner, Rudolf 1953- |
| author_role | aut aut aut |
| author_sort | Hlawka, Edmund 1916-2009 |
| author_variant | e h eh j s js r t rt |
| building | Verbundindex |
| bvnumber | BV004627397 |
| classification_rvk | SK 180 |
| ctrlnum | (OCoLC)439214418 (DE-599)BVBBV004627397 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004627397 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:20:29Z |
| institution | BVB |
| isbn | 9783540520160 3540520163 0387520163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002842528 |
| oclc_num | 439214418 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-11 DE-188 DE-83 DE-20 |
| owner_facet | DE-384 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-706 DE-11 DE-188 DE-83 DE-20 |
| physical | X, 238 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spellingShingle | Hlawka, Edmund 1916-2009 Schoißengeier, Johannes 1948- Taschner, Rudolf 1953- Geometric and analytic number theory Analytische Zahlentheorie (DE-588)4001870-2 gnd Geometrie der Zahlen (DE-588)4227477-1 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| subject_GND | (DE-588)4001870-2 (DE-588)4227477-1 (DE-588)4067277-3 |
| title | Geometric and analytic number theory |
| title_alt | Geometrische und analytische Zahlentheorie |
| title_auth | Geometric and analytic number theory |
| title_exact_search | Geometric and analytic number theory |
| title_full | Geometric and analytic number theory Edmund Hlawka ; Johannes Schoissengeier ; Rudolf Taschner |
| title_fullStr | Geometric and analytic number theory Edmund Hlawka ; Johannes Schoissengeier ; Rudolf Taschner |
| title_full_unstemmed | Geometric and analytic number theory Edmund Hlawka ; Johannes Schoissengeier ; Rudolf Taschner |
| title_short | Geometric and analytic number theory |
| title_sort | geometric and analytic number theory |
| topic | Analytische Zahlentheorie (DE-588)4001870-2 gnd Geometrie der Zahlen (DE-588)4227477-1 gnd Zahlentheorie (DE-588)4067277-3 gnd |
| topic_facet | Analytische Zahlentheorie Geometrie der Zahlen Zahlentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002842528&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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