## ADDITIVE PROBLEMS WITH PRIME VARIABLES THE CIRCLE METHOD OF HARDY, RAMANUJAN AND LITTLEWOOD (2012)

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by
Alessandro Zaccagnini

### BibTeX

@MISC{Zaccagnini12additiveproblems,

author = {Alessandro Zaccagnini},

title = {ADDITIVE PROBLEMS WITH PRIME VARIABLES THE CIRCLE METHOD OF HARDY, RAMANUJAN AND LITTLEWOOD},

year = {2012}

}

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### Abstract

In these lectures we give an overview of the circle method introduced by Hardy and Ramanujan at the beginning of the twentieth century, and developed by Hardy, Littlewood and Vinogradov, among others. We also try and explain the main difficulties in proving Goldbach’s conjecture and we give a sketch of the proof of Vinogradov’s three-prime Theorem.