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Softcover ISBN:  9780821849422 
Product Code:  MMONO/13.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
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Product Code:  MMONO/13.S.E 
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MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821849422 
eBook ISBN:  9781470416218 
Product Code:  MMONO/13.S.B 
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MAA Member Price:  $288.00 $218.25 
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Book DetailsTranslations of Mathematical MonographsVolume: 13; 1965; 190 ppMSC: Primary 11
LooKeng 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 meanvalue theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the WaringGoldbach 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.

Table of Contents

Chapters

Trigonometric sums

Estimates for sums involving the divisor function $d(n)$

Meanvalue theorems for certain trigonometric sums (I)

Vinogradov’s meanvalue theorem and its corollaries

Meanvalue theorems for certain trigonometric sums (II)

Trigonometric sums depending on prime numbers

An asymptotic formula for the number of solutions of the WaringGoldbach problem

Singular series

A further study of the WaringGoldbach problem

Indeterminate equations in prime unknowns

A further study of the problem of the preceding chapter

Other results

Appendix


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LooKeng 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 meanvalue theorem for trigonometric sums, which Hua usefully rephrases and improves. Hua states a generalized version of the WaringGoldbach 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.

Chapters

Trigonometric sums

Estimates for sums involving the divisor function $d(n)$

Meanvalue theorems for certain trigonometric sums (I)

Vinogradov’s meanvalue theorem and its corollaries

Meanvalue theorems for certain trigonometric sums (II)

Trigonometric sums depending on prime numbers

An asymptotic formula for the number of solutions of the WaringGoldbach problem

Singular series

A further study of the WaringGoldbach problem

Indeterminate equations in prime unknowns

A further study of the problem of the preceding chapter

Other results

Appendix