Requesting constructive criticism for my paper

[sbrothy]

Heh, I'm immensely proud I could contribute with anything at all. That will keep me going all week. :)

 

[mathhabibi]

Another idea is to check functions $f(k)=\sum_{m=1}^k \dfrac{(-1)^{m+1}}{m}$ where $\lim_{n \to \infty}f(n)$ depends on the ordering of the sum.

I didn’t see this edit, I devoted half a subsection on this specific function (the alternating harmonic numbers) and came up with a conjecture on its zeroes and a reflection formula for it

 

[Mark44]

You mention Riemann, Euler, MacLauri and Ramanjuan but don't cite them.

Maybe something from Ramanujan, but Riemann, Euler, and Maclaurin don't need specific citations, IMO. Every calculus book mentions the Riemann integral and Maclaurin series, as well as Euler's equation involving $e, \pi, -1, i$ and $0$ without citing the work in which these first appeared.

 

[mathhabibi]

Maybe something from Ramanujan, but Riemann, Euler, and Maclaurin don't need specific citations, IMO. Every calculus book mentions the Riemann integral and Maclaurin series, as well as Euler's equation involving $e, \pi, -1, i$ and $0$ without citing the work in which these first appeared.

No, there isn't a Riemann integral or Maclaurin series. It's the Riemann zeta function and Euler-Maclaurin formula. But again, these two are pretty well-known already.

 

[Mark44]

No, there isn't a Riemann integral or Maclaurin series. It's the Riemann zeta function and Euler-Maclaurin formula. But again, these two are pretty well-known already.

I gave those as examples, but my point was that these names are so well-known, that citations aren't necessary.

 

[mathhabibi]

After taking in all your feedback, I submitted a new version of my paper, where instead the main result is called the simple result and is defined as a lemma, not a theorem. I also solved the "conjecture" in my paper and replaced it with a theorem, deriving an asymptotic for the roots of the Alternating Harmonic Numbers. I appreciate your feedback, it made a difference (for me at least)!

One small note, I wasn't able to cite Ramanujan because his Ramanujan summation appears in his notebooks, and I don't know how to cite them as they're unpublished. Hopefully mentioning his name in "Ramanujan Summation" should be enough to give him proper credit.

 

[sbrothy]

I appreciate the little heads-up. Don't worry. I'm under no illusions that I can really contribute anything. All the best. :)

 

[mathhabibi]

I appreciate the little heads-up. Don't worry. I'm under no illusions that I can really contribute anything. All the best. :)

I think I can still cite his notebooks somehow. You have contributed something, don't downplay what you've done :)