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Author | : Luogeng Hua |
Publisher | : American Mathematical Soc. |
Total Pages | : 206 |
Release | : 2009-12-04 |
Genre | : Mathematics |
ISBN | : 0821849425 |
Download Additive Theory of Prime Numbers Book in PDF, ePub and Kindle
Loo-Keng Hua was a master mathematician, best known for his work using analytic methods in number theory. In particular, Hua is remembered for his contributions to Waring's Problem and his estimates of trigonometric sums. Additive Theory of Prime Numbers is an exposition of the classic methods as well as Hua's own techniques, many of which have now also become classic. An essential starting point is Vinogradov's mean-value theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the Waring-Goldbach problem and gives asymptotic formulas for the number of solutions in Waring's Problem when the monomial $x^k$ is replaced by an arbitrary polynomial of degree $k$. The book is an excellent entry point for readers interested in additive number theory. It will also be of value to those interested in the development of the now classic methods of the subject.
Author | : L. K. Hua |
Publisher | : |
Total Pages | : 190 |
Release | : 1965 |
Genre | : |
ISBN | : |
Download Additive Theory of prime Numbers Book in PDF, ePub and Kindle
Author | : Jianya Liu |
Publisher | : World Scientific Publishing Company Incorporated |
Total Pages | : 200 |
Release | : 2020-02-28 |
Genre | : Mathematics |
ISBN | : 9789812775924 |
Download New Developments in the Additive Theory of Prime Numbers Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 190 |
Release | : 1966 |
Genre | : |
ISBN | : |
Download Additive theory of prime numbers Book in PDF, ePub and Kindle
Author | : Melvyn B. Nathanson |
Publisher | : Springer Science & Business Media |
Total Pages | : 350 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 1475738455 |
Download Additive Number Theory The Classical Bases Book in PDF, ePub and Kindle
[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.
Author | : Loo-Keng Hua |
Publisher | : |
Total Pages | : 190 |
Release | : 1966 |
Genre | : |
ISBN | : |
Download Additive theory of prime numbers Book in PDF, ePub and Kindle
Author | : Warner Berthoff |
Publisher | : |
Total Pages | : |
Release | : 1965 |
Genre | : |
ISBN | : |
Download Additive Theory of Prime Numbers Book in PDF, ePub and Kindle
Author | : Loo-Keng Hua (Mathematician, China) |
Publisher | : |
Total Pages | : 0 |
Release | : 1966 |
Genre | : |
ISBN | : |
Download Additive Theory of Prime Numbers Book in PDF, ePub and Kindle
Author | : Hou Loo Keng |
Publisher | : |
Total Pages | : 206 |
Release | : 1953 |
Genre | : |
ISBN | : |
Download Additive Theory of Prime Numbers Book in PDF, ePub and Kindle
Author | : Lo-Keng Hua |
Publisher | : |
Total Pages | : 13 |
Release | : 1965 |
Genre | : |
ISBN | : |
Download Additive Theory of Prime Numbers. Hua Book in PDF, ePub and Kindle