# Tag Archives: research

## Math journals and the fight over open access

Some may have heard me talk about this before, but I’ve caught the open source bug. At least, I’ve caught the collaboration and free-dissemination bug. And I don’t just mean software – there’s much more to open source than software (even though the term open source originated in reference to free access to source code). I use open source to refer to the idea that when someone consumes a product, they should have access to the design and details of implementation, and should be able to freely distribute the product whenever this is possible. In some ways, I’m still learning. For example, though I use linux, I do not know enough about coding to contribute actual code to the linux/unix community. But I know just enough python to contribute to Sage, and do. And I’m getting better.

I also believe in open access, which feels like a natural extension. By open access, I mean free access to peer-reviewed scholarly journals and other materials. It stuns me that the public does not generally have access to publicly-funded research. How is this acceptable? Another thing that really gets to me is how selling overpriced and overlarge calculus textbooks can allow the author to do things like spend 30+ million dollars on his home? This should not happen. At least, it shouldn’t happen now, in the internet age. All the material is freely available in at least as good of a presentation, so the cost of the textbook is a compilation cost (not worth over \$100). But these books are printed oversize, 1000+ pages, in full color and on 60-pound paper. That’s a recipe for high cost! It’s tremendously unfortunate, as it’s not as though the students even have a choice over what book they buy. But this is not the argument I want to make today, and I digress.

Recently, I was dragged down a rabbit hole. And what I saw when I emerged on the other side made me learn about a side of math journals I’d never seen before, and the fight over open access. I’d like to comment on this today – that’s after the fold.

## 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 $\displaystyle \sum_{nk^j \leq x} f(n) = a_1x + O(x^{1-\epsilon}) \iff \sum_{n \leq x} f(n) = \frac{a_1x}{\zeta(j)} + O(x^{1 – \epsilon})$.