Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields
In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math><...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/15/1710 |
| _version_ | 1797525346149466112 |
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| author | Nicuşor Minculete Diana Savin |
| author_facet | Nicuşor Minculete Diana Savin |
| author_sort | Nicuşor Minculete |
| collection | DOAJ |
| description | In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, and the generalized function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> in algebraic number fields. |
| first_indexed | 2024-03-10T09:12:30Z |
| format | Article |
| id | doaj.art-da8f8898d3334d41add728ee29b2af5a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:12:30Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-da8f8898d3334d41add728ee29b2af5a2023-11-22T05:55:28ZengMDPI AGMathematics2227-73902021-07-01915171010.3390/math9151710Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number FieldsNicuşor Minculete0Diana Savin1Faculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Street 50, 500091 Braşov, RomaniaFaculty of Mathematics and Computer Science, Transilvania University, Iuliu Maniu Street 50, 500091 Braşov, RomaniaIn this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula>, and the generalized function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> in algebraic number fields.https://www.mdpi.com/2227-7390/9/15/1710arithmetic functionsalgebraic number fieldsDedekind rings |
| spellingShingle | Nicuşor Minculete Diana Savin Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields Mathematics arithmetic functions algebraic number fields Dedekind rings |
| title | Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields |
| title_full | Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields |
| title_fullStr | Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields |
| title_full_unstemmed | Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields |
| title_short | Some Properties of Euler’s Function and of the Function <i>τ</i> and Their Generalizations in Algebraic Number Fields |
| title_sort | some properties of euler s function and of the function i τ i and their generalizations in algebraic number fields |
| topic | arithmetic functions algebraic number fields Dedekind rings |
| url | https://www.mdpi.com/2227-7390/9/15/1710 |
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