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Musings of the Mercurial Mathematician | mercmath.wordpress.com Reviews
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The circle method 1: Sums of 5 or more squares | Musings of the Mercurial Mathematician
https://mercmath.wordpress.com/2011/05/05/the-circle-method-1-sums-of-5-or-more-squares
Musings of the Mercurial Mathematician. The circle method 1: Sums of 5 or more squares. This is our first step in solving Waring’s problem. In particular, we’ll study the problem for degree 2. Later, we’ll combine these methods with Weyl’s inequality for higher degree exponential sums to solve Waring’s problem. We want to understand the asymptotics of. The number of ways to represent a number. As a sum of. Squares, i.e. We will solve this problem in dimensions. Using the Hardy-Littlewood circle method.
The circle method 0: Introducing Waring’s problem | Musings of the Mercurial Mathematician
https://mercmath.wordpress.com/2011/04/13/the-circle-method-0-introducing-warings-problem
Musings of the Mercurial Mathematician. The circle method 0: Introducing Waring’s problem. It’s a classical problem in number theory to ask which integers. Can be represented by a sum of squares. After a little bit of playing with sums of two squares, one might be led to conjecture the following theorem. Can be represented as a sum of two squares precisely when. Is of the form. Is a prime congruent to 1 mod 4. Every natural number is the sum of at most 4 squares. Later, the 3 squares question was solved.
The circle method 2: Elementary estimates for the singular series for sums of 5 or more squares | Musings of the Mercurial Mathematician
https://mercmath.wordpress.com/2011/07/01/the-circle-method-2-elementary-estimates-for-the-singular-series-for-sums-of-5-or-more-squares
Musings of the Mercurial Mathematician. The circle method 2: Elementary estimates for the singular series for sums of 5 or more squares. This is the long-awaited second step in solving Waring’s problem. Continuing our study of the sum of squares problem. In this post, we’ll analyze the singular series to show that we have a genuine asymptotic when. And what we’ve already shown. We want to understand the asymptotics of. The number of ways to represent a number. As a sum of. Squares, i.e. Is the normalized...
Update: New Year’s Resolution 2011 | Musings of the Mercurial Mathematician
https://mercmath.wordpress.com/2011/07/01/update-new-years-resolution-2011
Musings of the Mercurial Mathematician. Update: New Year’s Resolution 2011. I’m working on my third installment of my series of Hardy–Littlewood posts. Currently, there will be at least 6 posts in this series including the 0th post. I’ve understood better the Euclidean problem of spherical averages, but luckily, T. Tao wrote an excellent blog post. OK, back to work. Working is much harder now that Google has been released =). Leave a Reply Cancel reply. Enter your comment here. Packing planes in R 3.
Packing planes in R^3 | Musings of the Mercurial Mathematician
https://mercmath.wordpress.com/2011/10/04/packing-planes-in-r3
Musings of the Mercurial Mathematician. Packing planes in R 3. In these notes I’ll discuss Marstrand’s work on packing planes in. I follow very closely Marstrand’s approach and at the moment, I’m not making any effort to keep the exposition self-contained – sorry. In a later post, I plan to describe Falconer’s theorem on packing k-planes in. All measures will refer to Lebesgue or (in the case of the 2-sphere. Has measure 0, then for almost all directions. In a set of planar measure 0. With measure 0; let.
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Musings of the Mercurial Mathematician
Musings of the Mercurial Mathematician. Packing planes in R 3. In these notes I’ll discuss Marstrand’s work on packing planes in. I follow very closely Marstrand’s approach and at the moment, I’m not making any effort to keep the exposition self-contained – sorry. In a later post, I plan to describe Falconer’s theorem on packing k-planes in. All measures will refer to Lebesgue or (in the case of the 2-sphere. Has measure 0, then for almost all directions. In a set of planar measure 0. With measure 0; let.
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