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GCD Grid on the Front Cover
- tzs 5y ago> I strongly recommend this book to anyone who wants to learn analytic number theory For those who fall into that category but their calculus is rusty (or nonexistent), don't worry. From the book's preface: > Actually, a great deal of the book requires no calculus at all and could profitably be studied by sophisticated high school students. That said, it kicked my ass when I tried to read it during my first year in college. I don't know if that is because I was not as good as a sophisticated high school student, or because my actual classes didn't leave enough time or energy for reading a book like that recreationally.
- susam 5y agoWhile the claim in the preface that a great deal of the book requires no calculus is correct, I found that some of the very important theorems in the book depend heavily on calculus. Further, as soon as the text begins discussing analytic continuation of the zeta function, there is heavy usage of contour integrals. I had to brush up on complex analysis in order to make sense of the text. In case anyone is interested, I have taken a large number of notes that illustrate many theorems in the book with concrete examples. These examples may help in "visualizing" the theorems. The notes are available here: https://offbeat.cc/iant/boards/ https://offbeat.cc/iant/boards/. These notes also elaborate several intermediate steps of various proofs that are not explicitly expressed in the book.
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- karmakaze 5y agoI prefer a simpler interpretation of: > Then a box exists at if and only if gcd(x, y) != 1 and we can consider anything that is not 1 (i.e. undefined) to result in a box.