Generating Special Arithmetic Functions by Lambert Series Factorizations

2017/06/01 by Mircea Merca, Merca, Mircea, Maxie D. Schmidt +1
Engineering · Physics and Astronomy · #05A17 #05A19 #11A25 #11P81 #Advanced Mathematical Theories and Applications #Experimental and Theoretical Physics Studies #FOS: Mathematics #Number Theory (math.NT) #Sports Dynamics and Biomechanics

paper · pdf · doi:10.48550/arxiv.1706.00393

openalex publication_date 2017/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We summarize the known useful and interesting results and formulas we have discovered so far in this collaborative article summarizing results from two related articles by Merca and Schmidt arriving at related so-termed Lambert series factorization theorems. We unify the matrix representations that underlie two of our separate papers, and which commonly arise in identities involving partition functions and other functions generated by Lambert series. We provide a number of properties and conjectures related to the inverse matrix entries defined in Schmidt's article and the Euler partition function p(n) which we prove through our new results unifying the expansions of the Lambert series factorization theorems within this article.

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