Non-factorizable C-valued functions induced by finite connected graphs
In this paper, we study factorizability of \(\mathbb{C}\)-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta fun...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2017-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol37/2/art/opuscula_math_3709.pdf |
| _version_ | 1818854305291042816 |
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| author | Ilwoo Cho |
| author_facet | Ilwoo Cho |
| author_sort | Ilwoo Cho |
| collection | DOAJ |
| description | In this paper, we study factorizability of \(\mathbb{C}\)-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta functions. In particular, we are interested in (i) "non-factorizability" of such functions, and (ii) certain factorizable functions induced by non-factorizable functions. By constructing factorizable functions from our non-factorizable functions, we study relations between graph zeta functions and well-known number-theoretic objects, the Riemann zeta function and the Euler totient function. |
| first_indexed | 2024-12-19T07:50:36Z |
| format | Article |
| id | doaj.art-494cc88f62a7480fbe29e0b136ba4098 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-19T07:50:36Z |
| publishDate | 2017-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-494cc88f62a7480fbe29e0b136ba40982022-12-21T20:30:11ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742017-01-01372225263http://dx.doi.org/10.7494/OpMath.2017.37.2.2253709Non-factorizable C-valued functions induced by finite connected graphsIlwoo Cho0St. Ambrose University, Department of Mathematics and Statistics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USAIn this paper, we study factorizability of \(\mathbb{C}\)-valued formal series at fixed vertices, called the graph zeta functions, induced by the reduced length on the graph groupoids of given finite connected directed graphs. The construction of such functions is motivated by that of Redei zeta functions. In particular, we are interested in (i) "non-factorizability" of such functions, and (ii) certain factorizable functions induced by non-factorizable functions. By constructing factorizable functions from our non-factorizable functions, we study relations between graph zeta functions and well-known number-theoretic objects, the Riemann zeta function and the Euler totient function.http://www.opuscula.agh.edu.pl/vol37/2/art/opuscula_math_3709.pdfdirected graphsgraph groupoidsRedei zeta functionsgraph zeta functionsnon-factorizable graphsgluing on graphs |
| spellingShingle | Ilwoo Cho Non-factorizable C-valued functions induced by finite connected graphs Opuscula Mathematica directed graphs graph groupoids Redei zeta functions graph zeta functions non-factorizable graphs gluing on graphs |
| title | Non-factorizable C-valued functions induced by finite connected graphs |
| title_full | Non-factorizable C-valued functions induced by finite connected graphs |
| title_fullStr | Non-factorizable C-valued functions induced by finite connected graphs |
| title_full_unstemmed | Non-factorizable C-valued functions induced by finite connected graphs |
| title_short | Non-factorizable C-valued functions induced by finite connected graphs |
| title_sort | non factorizable c valued functions induced by finite connected graphs |
| topic | directed graphs graph groupoids Redei zeta functions graph zeta functions non-factorizable graphs gluing on graphs |
| url | http://www.opuscula.agh.edu.pl/vol37/2/art/opuscula_math_3709.pdf |
| work_keys_str_mv | AT ilwoocho nonfactorizablecvaluedfunctionsinducedbyfiniteconnectedgraphs |