Does anyone know of applications of multiple sums of a sequence?
I know of the Multiple Zeta values (which is a multiple sum of 1/N^s). This has multiple applications in quantum physics, QED, QCD, connection between knot theory and quantum physics, ...
Does anyone know of potential applications for this more general form which is a general multiple sums? I have written an article about it and about its applications including partition identities, polynomial identities. I wanted to know if anyone know of applications outside mathematics or additional applications in math.
Dear Romeo Meštrović
I have just followed you in order to see your future updates. I have checked your profile and you seem to have a lot of articles. could you recommend the specific ones that would be of interest to me.
Thank you.
From financial mathematics, the series where a_n = n(1+r)^(1-n) occurs in calculating the duration of a bond.
Can you recommend any link or article?
The multiple sums of that a_n is used in finance? Douglass Grant
I have 2 articles about multiple sums on my profile entitled “Multiple Sums and Partition Identities“ and “Recurrent Sums and Partition Identities”. Can you check them and confirm that we are talking about the same type of sums.
Dear Roudy El Haddad
It seems that the article shows hard, excellent work.
Before asking about any potential applications, one needs to check the work's correctness and originality.
Have you submitted your article to any Journal?
Meanwhile, I will read your article as soon as I can and then show you some suggestions about the possible application in Number Theory.
Best regards
Dear Issam Kaddoura
i have sent both articles to a journal I don’t know if I am allowed to give the name of the journal (because some journals consider that it might make the process biased).
Thank you for your response. I will be waiting for your futur comments on my article. Feel free to give me any feedback positive or negative.
To Roudy El Haddad:
Please see some my papers and related references, available at my RG profile https://www.researchgate.net/profile/Romeo_Mestrovic/research.
Dear Romeo Meštrović
I have just followed you in order to see your future updates. I have checked your profile and you seem to have a lot of articles. could you recommend the specific ones that would be of interest to me.
Thank you.
Dear Roudy El Haddad,
Also, please, see some my papers and preprints (mainly available at ArXiv.org) concerning divisibility properties (modulo primes or/and prime powers) of multiple harmonic sums, available at my Google Scholar profile, https://scholar.google.com/citations?hl=en&user=wE9XgSAAAAAJ, and some papers and one Phd Dissertation that were cited my papers (for example, the papers and Diisertation available at https://scholar.google.com/scholar?oi=bibs&hl=en&cites=6235527525856012264 and https://scholar.google.com/scholar?oi=bibs&hl=en&cites=15660953393028534549,11360213591323291155).
Dear Mirzakhmet Syzdykov
Could you recommend an article about the subject.
Thank you.
I have attached below two images which show the two types of multiple sums I am talking about. So that you could know exactly what structures I am discussing.
A particular case of these multiple sums is when a_N = 1/N^s. This case corresponds to the Multiple Zeta Values (MZVs) and Multiple Zeta Star Values (MZSVs). I know of a lot of applications for this type of sums from QED to QCD to the connection between quantum physics and knot theory. What I would like to know is if there are applications of this multiple sums structure for other sequences (other than 1/N^s).
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