John Knopfmacher

869 total citations
65 papers, 452 citations indexed

About

John Knopfmacher is a scholar working on Algebra and Number Theory, Mathematical Physics and Computational Theory and Mathematics. According to data from OpenAlex, John Knopfmacher has authored 65 papers receiving a total of 452 indexed citations (citations by other indexed papers that have themselves been cited), including 27 papers in Algebra and Number Theory, 24 papers in Mathematical Physics and 22 papers in Computational Theory and Mathematics. Recurrent topics in John Knopfmacher's work include Analytic Number Theory Research (12 papers), Advanced Mathematical Identities (11 papers) and advanced mathematical theories (9 papers). John Knopfmacher is often cited by papers focused on Analytic Number Theory Research (12 papers), Advanced Mathematical Identities (11 papers) and advanced mathematical theories (9 papers). John Knopfmacher collaborates with scholars based in South Africa, Australia and Germany. John Knopfmacher's co-authors include Arnold Knopfmacher, Helmut Prodinger, Guy Louchard, Wenbin Zhang, George E. Andrews, Wolfgang Schwarz, Allan M. Sinclair and Toufik Mansour and has published in prestigious journals such as Journal of Mathematical Analysis and Applications, Journal of Computational and Applied Mathematics and Acta Mathematica.

In The Last Decade

John Knopfmacher

57 papers receiving 380 citations

Peers

John Knopfmacher
Kirby A. Baker United States
Ralph Freese United States
Bolyai János Matematikai Társulat
Robert I. Jewett United States
Boaz Tsaban Israel
Boban Veličković France
James H. Schmerl United States
P. D. T. A. Elliott United States
Peter Crawley United States
Yu. L. Ershov Russia
Kirby A. Baker United States
John Knopfmacher
Citations per year, relative to John Knopfmacher John Knopfmacher (= 1×) peers Kirby A. Baker

Countries citing papers authored by John Knopfmacher

Since Specialization
Citations

This map shows the geographic impact of John Knopfmacher's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by John Knopfmacher with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites John Knopfmacher more than expected).

Fields of papers citing papers by John Knopfmacher

Since Specialization
Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by John Knopfmacher. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by John Knopfmacher. The network helps show where John Knopfmacher may publish in the future.

Co-authorship network of co-authors of John Knopfmacher

This figure shows the co-authorship network connecting the top 25 collaborators of John Knopfmacher. A scholar is included among the top collaborators of John Knopfmacher based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with John Knopfmacher. John Knopfmacher is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

20 of 20 papers shown
1.
Louchard, Guy, et al.. (2003). The Number of Inversions in Permutations: A Saddle Point Approach. Journal of integer sequences. 6. 28. 16 indexed citations
2.
Knopfmacher, John, et al.. (2002). Arithmetical Semigroups Related to Trees and Polyhedra, II — Maps on Surfaces. Mathematische Nachrichten. 235(1). 59–81. 1 indexed citations
3.
Knopfmacher, John. (2001). RECENT DEVELOPMENTS AND APPLICATIONS OF ABSTRACT ANALYTIC NUMBER THEORY. Quaestiones Mathematicae. 24(3). 291–307. 1 indexed citations
4.
Andrews, George E., Arnold Knopfmacher, & John Knopfmacher. (2000). Engel Expansions and the Rogers–Ramanujan Identities. Journal of Number Theory. 80(2). 273–290. 10 indexed citations
5.
Knopfmacher, Arnold & John Knopfmacher. (1999). Arithmetical Semigroups Related to Trees and Polyhedra. Journal of Combinatorial Theory Series A. 86(1). 85–102. 6 indexed citations
6.
Knopfmacher, John & Arnold Knopfmacher. (1992). Metric properties of algorithms inducing Lüroth series expansions of Laurent series. French digital mathematics library (Numdam). 1 indexed citations
7.
Knopfmacher, Arnold & John Knopfmacher. (1992). Infinite series expansions forp-adic numbers. Journal of Number Theory. 41(2). 131–145. 1 indexed citations
8.
Knopfmacher, Arnold & John Knopfmacher. (1991). The number of steps in the euclidean algorithm over complex quadratic fields. BIT Numerical Mathematics. 31(2). 286–292. 2 indexed citations
9.
Knopfmacher, Arnold, et al.. (1990). Unique factorizations of formal power series. Journal of Mathematical Analysis and Applications. 149(2). 402–411. 4 indexed citations
10.
Knopfmacher, Arnold & John Knopfmacher. (1990). The distribution of values of polynomials over a finite field. Linear Algebra and its Applications. 134. 145–151. 4 indexed citations
11.
Knopfmacher, Arnold, et al.. (1990). Lüroth-type alternating series representations for real numbers. Acta Arithmetica. 55(4). 311–322. 16 indexed citations
12.
Knopfmacher, Arnold & John Knopfmacher. (1989). Infinite products for power series. Journal of Approximation Theory. 59(3). 276–281. 3 indexed citations
13.
Knopfmacher, Arnold & John Knopfmacher. (1989). Series expansions in p-adic and other non-archimedean fields. Journal of Number Theory. 32(3). 297–306. 5 indexed citations
14.
Knopfmacher, Arnold & John Knopfmacher. (1988). A product representation for power series. Complex Variables Theory and Application An International Journal. 10(4). 283–294. 1 indexed citations
15.
Knopfmacher, John. (1985). Direct factors of polynomial rings over finite fields. Journal of Combinatorial Theory Series A. 40(2). 429–434. 1 indexed citations
16.
Knopfmacher, John. (1977). An abstract prime number theorem relating to algebraic function fields. Archiv der Mathematik. 29(1). 271–279. 5 indexed citations
17.
Knopfmacher, John. (1976). Arithmetical properties of finite graphs and polynomials. Journal of Combinatorial Theory Series B. 20(3). 205–215. 2 indexed citations
18.
Knopfmacher, John. (1975). On measures of fuzziness. Journal of Mathematical Analysis and Applications. 49(3). 529–534. 94 indexed citations
19.
Knopfmacher, John. (1969). On Lie algebra obstructions. Bulletin of the Australian Mathematical Society. 1(2). 281–288. 1 indexed citations
20.
Knopfmacher, John. (1960). 2874. A note on perfect numbers. The Mathematical Gazette. 44(347). 45–45. 2 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

Explore authors with similar magnitude of impact

Breakdown of academic impact, for papers by Kirby A. Baker Breakdown of academic impact, for papers by Ralph Freese Breakdown of academic impact, for papers by Bolyai János Matematikai Társulat Breakdown of academic impact, for papers by Robert I. Jewett Breakdown of academic impact, for papers by Boaz Tsaban Breakdown of academic impact, for papers by Boban Veličković Breakdown of academic impact, for papers by James H. Schmerl Breakdown of academic impact, for papers by P. D. T. A. Elliott Breakdown of academic impact, for papers by Peter Crawley Breakdown of academic impact, for papers by Yu. L. Ershov
Rankless by CCL
2026