Topic
Euler function
About: Euler function is a research topic. Over the lifetime, 389 publications have been published within this topic receiving 4003 citations.
Papers published on a yearly basis
Papers
TL;DR: An extension of Euler's gamma function and Riemann's zeta function, for which the usual properties and representation are naturally and simply extended, is introduced in this paper.
276 citations
TL;DR: The perfectness of X_n is decided and it is shown that all nonzero eigenvalues of $X_n$ are integers dividing the value $\varphi(n)$ of the Euler function.
Abstract: The unitary Cayley graph $X_n$ has vertex set $Z_n=\{0,1, \ldots ,n-1\}$. Vertices $a, b$ are adjacent, if gcd$(a-b,n)=1$. For $X_n$ the chromatic number, the clique number, the independence number, the diameter and the vertex connectivity are determined. We decide on the perfectness of $X_n$ and show that all nonzero eigenvalues of $X_n$ are integers dividing the value $\varphi(n)$ of the Euler function.
179 citations
TL;DR: In this paper, the divisibility of the Ramanujan type of the function a(n) defined by √ √ n √ q √ (q;q)^{-1}_\infty (q^2; q^2)^{ − 1}_ √ 0.
Abstract: In this paper, we study the divisibility of the function a(n) defined by $\sum_{n\geq 0} a(n) q^n := (q;q)^{-1}_\infty (q^2; q^2)^{-1}_\infty $. In particular, we prove certain "Ramanujan type cong...
79 citations
TL;DR: Partition-theoretic interpretation of two truncated identities of Gauss solving a problem by Guo and Zeng are provided and it is revealed that these results are essentially corollaries of the RogersFine identity.
74 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 12 |
| 2020 | 6 |
| 2019 | 8 |
| 2018 | 9 |
| 2017 | 9 |
| 2016 | 8 |