Additive Number Theory: The Classical Bases
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
1996
|
| Series: | Graduate Texts in Mathematics
164 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | [Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture |
| Physical Description: | 1 Online-Ressource (XIV, 342 p) |
| ISBN: | 9781475738452 9781441928481 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-3845-2 |
Staff View
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| 500 | |a [Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| id | DE-604.BV042421535 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475738452 9781441928481 |
| issn | 0072-5285 |
| language | English |
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| spelling | Nathanson, Melvyn B. 1944- Verfasser (DE-588)121815226 aut Additive Number Theory The Classical Bases by Melvyn B. Nathanson New York, NY Springer New York 1996 1 Online-Ressource (XIV, 342 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 164 0072-5285 [Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture Mathematics Global analysis (Mathematics) Number theory Number Theory Analysis Mathematik Additive Zahlentheorie (DE-588)4141387-8 gnd rswk-swf Additive Zahlentheorie (DE-588)4141387-8 s 1\p DE-604 https://doi.org/10.1007/978-1-4757-3845-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nathanson, Melvyn B. 1944- Additive Number Theory The Classical Bases Mathematics Global analysis (Mathematics) Number theory Number Theory Analysis Mathematik Additive Zahlentheorie (DE-588)4141387-8 gnd |
| subject_GND | (DE-588)4141387-8 |
| title | Additive Number Theory The Classical Bases |
| title_auth | Additive Number Theory The Classical Bases |
| title_exact_search | Additive Number Theory The Classical Bases |
| title_full | Additive Number Theory The Classical Bases by Melvyn B. Nathanson |
| title_fullStr | Additive Number Theory The Classical Bases by Melvyn B. Nathanson |
| title_full_unstemmed | Additive Number Theory The Classical Bases by Melvyn B. Nathanson |
| title_short | Additive Number Theory |
| title_sort | additive number theory the classical bases |
| title_sub | The Classical Bases |
| topic | Mathematics Global analysis (Mathematics) Number theory Number Theory Analysis Mathematik Additive Zahlentheorie (DE-588)4141387-8 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Number theory Number Theory Analysis Mathematik Additive Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4757-3845-2 |
| work_keys_str_mv | AT nathansonmelvynb additivenumbertheorytheclassicalbases |