Additive Number Theory The Classical Bases

Front Cover
Springer Science & Business Media, Jun 25, 1996 - Mathematics - 342 pages
0 Reviews
[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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

III
3
IV
4
V
5
VI
7
VII
12
VIII
17
IX
24
X
27
LI
178
LII
186
LIII
191
LIV
195
LV
199
LVI
204
LVII
208
LIX
211

XI
33
XII
34
XIII
37
XIV
38
XV
44
XVI
49
XVII
71
XVIII
72
XIX
75
XXI
77
XXII
86
XXIII
94
XXV
97
XXVII
99
XXVIII
102
XXIX
103
XXX
111
XXXI
118
XXXIII
121
XXXV
124
XXXVI
125
XXXVII
127
XXXVIII
129
XXXIX
133
XL
137
XLI
146
XLII
147
XLIV
151
XLV
153
XLVI
158
XLVII
167
XLVIII
173
XLIX
174
L
177
LX
212
LXI
213
LXII
215
LXIII
220
LXIV
227
LXV
230
LXVII
231
LXVIII
238
LXIX
244
LXX
251
LXXI
259
LXXII
267
LXXIV
271
LXXV
272
LXXVI
275
LXXVII
279
LXXVIII
281
LXXIX
286
LXXX
292
LXXXI
297
LXXXII
298
LXXXIII
301
LXXXIV
303
LXXXV
308
LXXXVI
310
LXXXVII
314
LXXXVIII
317
LXXXIX
320
XC
323
XCI
327
XCIII
331
XCIV
341
Copyright

Other editions - View all

Common terms and phrases

References to this book

A Course in Convexity
Alexander Barvinok
No preview available - 2002
All Book Search results »

Bibliographic information