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I am a Math student and I am curious about the topics in this article. I am curious as to what all branches of Mathematics is the paper related to? It's a resu

by ksd482 7y ago

I am a Math student and I am curious about the topics in this article. I am curious as to what all branches of Mathematics is the paper related to? It's a result about polynomials, so Algebra and Analysis?

impendia 7y ago
This area is usually known as "additive combinatorics". https://en.wikipedia.org/wiki/Arithmetic_combinatorics https://en.wikipedia.org/wiki/Arithmetic_combinatorics
- ksd482 7y ago
  Thanks! The Math in that paper is mind boggling! I hope to get to a point to understand it someday. Very naive question: the paper uses integrals (perhaps Lebesgue --- can you tell how naive I am, yet?) for proving some lemmas etc. As a beginner it's hard for me to understand how integrals come into picture in number theory. Not that it is my plan to do so, can you tell me what all fields of Math (specifically textbooks) and techniques I need to be familiar with to understand the paper? For e.g., Abstract Algebra (D&F), Functional Analysis (graduate), Combinatorics etc.? This will give me a much clearer picture on how various fields of Mathematics come into play. Thanks again!
  - impendia 7y ago
    If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics. Dummit and Foote's Abstract Algebra is an excellent book -- even if not very directly relevant to additive combinatorics. Analysis background would be useful, such as to be found in Stein and Shakarchi's series. Some introductory combinatorics would also be good (e.g. Stanley's Enumerative Combinatorics, or Van Lint and Wilson). Finally, analytic number theory would also be good to learn. For example, you might read Davenport's Multiplicative Number Theory. (Especially if you want to see integrals come into the picture.)
    - ksd482 7y ago
      Thank you! This is exactly what I was looking for. This gives me a sense as to where I stand relative to understanding this paper.

by ksd482 7y ago

impendia 7y ago

This area is usually known as "additive combinatorics". https://en.wikipedia.org/wiki/Arithmetic_combinatorics https://en.wikipedia.org/wiki/Arithmetic_combinatorics

ksd482 7y ago
Thanks! The Math in that paper is mind boggling! I hope to get to a point to understand it someday. Very naive question: the paper uses integrals (perhaps Lebesgue --- can you tell how naive I am, yet?) for proving some lemmas etc. As a beginner it's hard for me to understand how integrals come into picture in number theory. Not that it is my plan to do so, can you tell me what all fields of Math (specifically textbooks) and techniques I need to be familiar with to understand the paper? For e.g., Abstract Algebra (D&F), Functional Analysis (graduate), Combinatorics etc.? This will give me a much clearer picture on how various fields of Mathematics come into play. Thanks again!
- impendia 7y ago
  If you want to understand Peluse's paper, I think the most directly relevant background reading would be Tao and Vu's Additive Combinatorics. Dummit and Foote's Abstract Algebra is an excellent book -- even if not very directly relevant to additive combinatorics. Analysis background would be useful, such as to be found in Stein and Shakarchi's series. Some introductory combinatorics would also be good (e.g. Stanley's Enumerative Combinatorics, or Van Lint and Wilson). Finally, analytic number theory would also be good to learn. For example, you might read Davenport's Multiplicative Number Theory. (Especially if you want to see integrals come into the picture.)
  - ksd482 7y ago
    Thank you! This is exactly what I was looking for. This gives me a sense as to where I stand relative to understanding this paper.