A generalization of a graph theory Mertens’ theorem: Galois covering case
| Autor: | Iwao Sato, Seiken Saito, Takehiro Hasegawa |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Mertens conjecture
Discrete mathematics Applied Mathematics General Mathematics Fundamental theorem of Galois theory 010102 general mathematics Galois group 0102 computer and information sciences 01 natural sciences Embedding problem Combinatorics Differential Galois theory symbols.namesake 010201 computation theory & mathematics Mertens function Mertens' theorems symbols Galois extension 0101 mathematics Mathematics |
| Zdroj: | Forum Mathematicum. 30:599-615 |
| ISSN: | 1435-5337 0933-7741 |
| Popis: | In 1874, Franz Mertens proved the so-called Mertens’ theorem, and in 1974, Kenneth S. Williams showed Mertens’ theorem associated with a character. In a previous paper, we presented a graph-theoretic analogue to Williams’ theorem. In this paper, we generalize our previous work in the sense that a character is extended to a representation. To our knowledge, a number-theoretic analogue to our result is not yet known. So, we expect that, by using our methods, it can be proven in the future. |
| Databáze: | OpenAIRE |
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