# 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 $\displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1 – \epsilon})$ for a fixed $j$ and a constant $a_1$, so that the sum is over both $n$ and $k$. We will see that $\displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1-\epsilon}) \iff \sum_{n \leq x} f(n) = \frac{a_1x}{\zeta(j)} + O(x^{1 – \epsilon})$.

## 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.

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