New Developments in the Additive Theory of Prime Numbers

New Developments in the Additive Theory of Prime Numbers

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Description

The Waring-Goldbach problem seeks to represent positive integers satisfying necessary congruence conditions by powers of primes. The circle method of Hardy and Littlewood in combination with the estimates of Vinogadov for exponential sums over primes gives an affirmative answer to the general Waring-Goldbach problem. In recent years, new ideas using the circle method, sieves, and exponential sums have been incorporated into the Waring-Goldbach problem, encouraging remarkable advances. The purpose of this book is to introduce some of these new ideas, illustrated by dealing with the Waring-Goldbach problem for lower degrees.show more

Product details

  • Hardback | 200 pages
  • World Scientific Publishing Co Pte Ltd
  • Singapore, Singapore
  • English
  • 9812775927
  • 9789812775924

Table of contents

The Riemann Zeta-Function and Dirichlet L-Functions; Sums of Two Squares, and of Two Squares of Primes; The Circle Method in the Waring-Goldbach Problem; The Large Sieve; The Major Arcs; Exponential Sums Over Primes; Sums of Squares of Primes; The Major Arcs, II; Introduction to Sieve Methods; Exponential Sums Over Primes, II; Sums of Cubes of Primes; Sums of Forth Powers of Primes; Sums of Fifth Powers of Primes; High Powers.show more