2

This question consists of a general question and a specific question. My general question is simple. Suppose I read a paper I like and I want to find out more about the topic. How can I do this ? The natural place to start is to go through the references at the end of the paper. However, there is a problem with this. References are only provided in one direction in time, namely the past. If the paper I'm reding was written in 1960, there's a good chance that extensive work has been done on the topic. How do I find references to how the topic has progressed after the paper has been published ?

Now, for my specific question, which is a special case of my general question. Courtesy of the wonderful Canadian Mathematical Society which allows free access to their back issues, I discovered a paper written in 1959 in the Canadian Mathematical Bulletin. The paper answers the question about how the set of non negative integers can be partitioned into two sets such that sums of pairs of distinct integers in both classes will be the same.

Here's a link to the paper. http://cms.math.ca/openaccess/cmb/v2/cmb1959v02.0085-0089.pdf

This paper is special to me, because it's the first research paper I read where I understood everything ! So, I was wondering if you guys could recommend some sources to me which either carry the problem forward, or which are written at the same level as this paper.

Daniel Robert-Nicoud
  • 29,795
Saikat
  • 2,461
  • I read somewhere (many years ago) that there was an effort to attack this kind of problem, creating lists of papers that cite a particular paper as a reference. I don't know what came of it. – Blue Jul 31 '16 at 11:39
  • @Blue Nice blog. I'm thinking of subscribing. What do you personally do when you face this problem ? – Saikat Jul 31 '16 at 11:47
  • 2
    look for a paper in google scholar, you can click "cited by" to get a list of papers that cite the given paper – Wouter Jul 31 '16 at 11:53
  • @user230452: Thanks for the blog-compliment ("blog-liment"?). I haven't written enough hard-core academic papers to have developed a robust forward-citation search strategy, so I can't offer specific tips. (BTW: I don't think Google Scholar was the initiative I mentioned before, but no matter. GS is now the name I'll attached to that memory. :) – Blue Jul 31 '16 at 12:41
  • @Blue Is it possible to subscribe to your blog for email notifications via Wordpress ? Earlier in the day, I was browsing a question on this site titled big list for math blogs and subscribed to them. I encourage you to post your blogs as answers to that question. – Saikat Jul 31 '16 at 12:53
  • If you have access to MathSciNet (which is the online version of Math Reviews), then you can look up the review of the paper, and it will have links to reviews of other papers that refer back to your paper. If you have access to a university library, they probably have access to MathSciNet. – Gerry Myerson Jul 31 '16 at 12:58
  • @user230452: Ah, thanks for the info. I haven't (yet) added a dedicated "subscribe" action to my blog, but you can always subscribe to it (or any other WP blog) via RSS using by attaching a "feed" parameter to the base URL: http://trigonography.com/?feed=rss2. I post links to https://twitter.com/trigonography, and (less-reliably) to https://facebook.com/trigonography/. I'll look into supporting email subscriptions. – Blue Jul 31 '16 at 13:18
  • @Blue Here's the link you should post about your blog to. http://math.stackexchange.com/questions/81/list-of-interesting-math-blogs . I don't know what RSS and WP is. Please elaborate on how I can subscribe to it. Throughly Feedly ? I understand running a blog is a lot of work, you don't have to put email notifications of it's too much to do :) – Saikat Jul 31 '16 at 14:36
  • @Blue The RSS button is opening in Podcasts app. Do you have a podcast ? For what it's worth, I added trigonometry and bloog to Wordpress, but it doesn't open the website when I click the link. Guess something's wrong. I don't log into Wordpress often and only keep track via email ... But, I'll try bookmarking the site. – Saikat Jul 31 '16 at 15:10
  • @user230452: No podcast. WP = WordPress. RSS = "Really Simple Syndication", which allows blogs and posts to be aggregated by "feed readers"; Here's short NYTimes article on RSS and some readers.. (It doesn't mention NetNewsWire (Mac/iOS), which is my reader of choice.) Finally, I've decided that I won't be doing email subscriptions for now. I don't want the responsibility of managing people's addresses; too many privacy/security concerns. I appreciate your interest! – Blue Jul 31 '16 at 20:51

2 Answers2

2

Concerning the specific question of the 1959 paper, here's a reviewer's note on MathSciNet, written by Ernst Straus:

"Reviewer's note: While the method of proof, by a clever use of generating functions, uses the fact that one is dealing with integers, the result is clearly valid for arbitrary infinite cyclic semi-groups and, by an obvious extension, for direct products of such semi-groups. This includes the case of the natural numbers under multiplication which is treated separately in the paper."

The paper is referred to in reviews of two other papers:

MR0399468 (53 #3312) Straus, E. G. Real analytic functions as ratios of absolutely monotonic functions. Spline functions and approximation theory (Proc. Sympos., Univ. Alberta, Edmonton, Alta., 1972), pp. 359–370. Internat. Ser. Numer. Math., Vol. 21, Birkhäuser, Basel, 1973.

MR0492264 (58 #11408) Goldstein, R. On meromorphic solutions of certain functional equations. Aequationes Math. 18 (1978), no. 1-2, 112–157.

Also, this paper cites Lambek-Moser in its references:

MR2014728 (2004m:68172) Allouche, Jean-Paul; Shallit, Jeffrey The ring of k-regular sequences. II. Words. Theoret. Comput. Sci. 307 (2003), no. 1, 3–29.

Gerry Myerson
  • 179,216
1

I don't know much about number theory, so i will only give a possible answer to the first, more general question (which probably deserves a thread on its own).

One possibility I know of is to use paperscape. Paperscape is a "landscape representation" of arXiv (basically a huge graph), clustering together related papers. There is also the very nice function allowing you to select a paper and "export it" to my.paperscape, where you can see all other papers cited and citing it.

Of course, the disadvantage is that you only get to see paper that are on arXiv.

Daniel Robert-Nicoud
  • 29,795