On Certain Generalizations of Rational and Irrational Equivariant Functions
In this paper, we address the case of a particular class of function referred to as the rational equivariant functions. We investigate which elliptic zeta functions arising from integrals of power of <i>℘</i>, where <i>℘</i> is the Weierstrass <i>℘</i>-function at...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2247 |
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| author | Isra Al-Shbeil Afis Saliu Abbas Kareem Wanas Adriana Cătaş |
| author_facet | Isra Al-Shbeil Afis Saliu Abbas Kareem Wanas Adriana Cătaş |
| author_sort | Isra Al-Shbeil |
| collection | DOAJ |
| description | In this paper, we address the case of a particular class of function referred to as the rational equivariant functions. We investigate which elliptic zeta functions arising from integrals of power of <i>℘</i>, where <i>℘</i> is the Weierstrass <i>℘</i>-function attached to a rank two lattice of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">C</mi></semantics></math></inline-formula>, yield rational equivariant functions. Our concern in this survey is to provide certain examples of rational equivariant functions. In this sense, we establish a criterion in order to determine the rationality of equivariant functions derived from ratios of modular functions of low weight. Modular forms play an important role in number theory and many areas of mathematics and physics. |
| first_indexed | 2024-03-09T12:46:47Z |
| format | Article |
| id | doaj.art-5e4ebd7841d04bc9830ab5b04a3669f0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:46:47Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5e4ebd7841d04bc9830ab5b04a3669f02023-11-30T22:11:42ZengMDPI AGMathematics2227-73902022-06-011013224710.3390/math10132247On Certain Generalizations of Rational and Irrational Equivariant FunctionsIsra Al-Shbeil0Afis Saliu1Abbas Kareem Wanas2Adriana Cătaş3Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanDepartment of Mathematics, University of the Gambia, Birkama Campus, MDI Road, Kanifing P.O. Box 3530, The GambiaDepartment of Mathematics, College of Science, University of Al-Qadisiyah, Al Diwaniyah 58801, IraqDepartment of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, RomaniaIn this paper, we address the case of a particular class of function referred to as the rational equivariant functions. We investigate which elliptic zeta functions arising from integrals of power of <i>℘</i>, where <i>℘</i> is the Weierstrass <i>℘</i>-function attached to a rank two lattice of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">C</mi></semantics></math></inline-formula>, yield rational equivariant functions. Our concern in this survey is to provide certain examples of rational equivariant functions. In this sense, we establish a criterion in order to determine the rationality of equivariant functions derived from ratios of modular functions of low weight. Modular forms play an important role in number theory and many areas of mathematics and physics.https://www.mdpi.com/2227-7390/10/13/2247rational equivariant functionselliptic zeta functionsmeromorphic functionWeierstrass ℘-function |
| spellingShingle | Isra Al-Shbeil Afis Saliu Abbas Kareem Wanas Adriana Cătaş On Certain Generalizations of Rational and Irrational Equivariant Functions Mathematics rational equivariant functions elliptic zeta functions meromorphic function Weierstrass ℘-function |
| title | On Certain Generalizations of Rational and Irrational Equivariant Functions |
| title_full | On Certain Generalizations of Rational and Irrational Equivariant Functions |
| title_fullStr | On Certain Generalizations of Rational and Irrational Equivariant Functions |
| title_full_unstemmed | On Certain Generalizations of Rational and Irrational Equivariant Functions |
| title_short | On Certain Generalizations of Rational and Irrational Equivariant Functions |
| title_sort | on certain generalizations of rational and irrational equivariant functions |
| topic | rational equivariant functions elliptic zeta functions meromorphic function Weierstrass ℘-function |
| url | https://www.mdpi.com/2227-7390/10/13/2247 |
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