Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Introduction
- 2 The Sieves of Brun and Selberg
- 3 Early Work
- 4 The Breakthrough of Goldston, Motohashi, Pintz and Yildirim
- 5 The Astounding Result of Yitang Zhang
- 6 Maynard’s Radical Simplification
- 7 Polymath’s Refinements of Maynards Results
- 8 Variations on Bombieri–Vinogradov
- 9 Further Work and the Epilogue
- Appendix A Bessel Functions of the First Kind
- Appendix B A Type of Compact Symmetric Operator
- Appendix C Solving an Optimization Problem
- Appendix D A Brun–Titchmarsh Inequality
- Appendix E The Weil Exponential Sum Bound
- Appendix F Complex Function Theory
- Appendix G The Dispersion Method of Linnik
- Appendix H One Thousand Admissible Tuples
- Appendix I PGpack Minimanual
- References
- Index
Appendix G - The Dispersion Method of Linnik
Published online by Cambridge University Press: 10 September 2021
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Introduction
- 2 The Sieves of Brun and Selberg
- 3 Early Work
- 4 The Breakthrough of Goldston, Motohashi, Pintz and Yildirim
- 5 The Astounding Result of Yitang Zhang
- 6 Maynard’s Radical Simplification
- 7 Polymath’s Refinements of Maynards Results
- 8 Variations on Bombieri–Vinogradov
- 9 Further Work and the Epilogue
- Appendix A Bessel Functions of the First Kind
- Appendix B A Type of Compact Symmetric Operator
- Appendix C Solving an Optimization Problem
- Appendix D A Brun–Titchmarsh Inequality
- Appendix E The Weil Exponential Sum Bound
- Appendix F Complex Function Theory
- Appendix G The Dispersion Method of Linnik
- Appendix H One Thousand Admissible Tuples
- Appendix I PGpack Minimanual
- References
- Index
Summary
This appendix first defines a form of the disperson method of Linnik for a particular class of integer equations, and then gives the result of its application to several examples due to Linnik, namely to an additive divisor problem, to norms in different algebraic number fields,counting the number of solutions to expressing a natural number as a sum of two squares plus an 2-almost prime, and to a Titchmarsh divisor problem. A not well known conjecture of Euler is stated as a challenge problem for the method.
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- Bounded Gaps Between PrimesThe Epic Breakthroughs of the Early Twenty-First Century, pp. 522 - 527Publisher: Cambridge University PressPrint publication year: 2021