I read the phrase Hardy-Littlewood circle method in many places in Analytic number theory books and papers. I would like to know why it is called circle method, what is the idea behind it? Is it possible to visualize it? Is there any lecture note or other reference that explains it. I read Iwaniec-Kowalski book in ANT but I did not get where the circle comes from, it says something in Cauchy integral formula, but I like to see more visualize.
Also I did not understand exactly the meaning and reason of calling major arc and minor arc how to choose in practice which arc is major and which is minor, in this method?
Thanks for any help.