Tag Archives: David Lowry

An Application of Mobius Inversion to Certain Asymptotics I

In this note, I consider an application of generalized Mobius Inversion to extract information of arithmetical sums with asymptotics of the form $latex \displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1 – \epsilon})$ for a fixed $latex j$ and a constant $latex a_1$, so that the sum is over both $latex n$ and $latex k$. We will see that $latex \displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1-\epsilon}) \iff \sum_{n \leq x} f(n) = \frac{a_1x}{\zeta(j)} + O(x^{1 – \epsilon})$.

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Math 90: Week 1

This is a post related to how I plan to conduct my [Math 90] TA sessions. I would like to use this space as a supplement to the class work. Each Tuesday night, after my recitations, I will post my worksheets and their solutions under a new page. That page will serve as a comment-forum for for any questions students may have over that week. I will answer any comments posted here periodically throughout the week. It is also possible I may post additional, supplementary materials here if I feel it necessary.

Now I ask that my students please do the following:

Below, you’ll see a comment form. Write a comment using your name (this will be displayed by each comment you make), your email address (this is not displayed publicly), and a comment. Write anything you’d like.If you need a prompt, write what you want to get out of this course, or ask me a question.

You can write mathy things on this forum using the $latex \LaTeX$ formatting language. A bit more on that here, except that to product inline formulas with $latex \$ \text{latex (code)} \$ $ (dollar sign, the word latex, the code, followed by a dollar sign). For example, we’ll be doing things like $latex \displaystyle \int_0^1 x^2 dx$ and $latex \displaystyle \sum_{n = 1}^N \left( \frac{1}{N}\right)f\left( \frac{n}{N}\right)$ in this course.

I look forward to seeing all of you in class. Please note that it will always be easy to check out my [Math 90] posthead by clicking on Math 90 in my pages menu at the top left, or by remembering that link. There will be links to the different pages from the posthead, once there are different pages to link to.

Posted in Brown University, Math 90 | Tagged , , , , , , | 11 Comments