Transcendental solutions of Fermat-type functional equations in Cn
The equation f n + g n = 1 can be interpreted as the Fermat Diophantine equation x n + y n = 1 within the function field when n is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polyn...
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| Veröffentlicht in: | Analysis and mathematical physics 2023, Vol.13 (5) |
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| container_title | Analysis and mathematical physics |
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| creator | Ahamed, Molla Basir Allu, Vasudevarao |
| description | The equation
f
n
+
g
n
=
1
can be interpreted as the Fermat Diophantine equation
x
n
+
y
n
=
1
within the function field when
n
is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polynomial coefficients in
C
n
. If the coefficients of the equation are transcendental functions and satisfy a certain relationship, we show that transcendental solutions can be obtained. Moreover, we determine the precise form of the solutions in both cases. |
| doi_str_mv | 10.1007/s13324-023-00828-4 |
| format | Article |
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f
n
+
g
n
=
1
can be interpreted as the Fermat Diophantine equation
x
n
+
y
n
=
1
within the function field when
n
is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polynomial coefficients in
C
n
. If the coefficients of the equation are transcendental functions and satisfy a certain relationship, we show that transcendental solutions can be obtained. Moreover, we determine the precise form of the solutions in both cases.</description><identifier>ISSN: 1664-2368</identifier><identifier>EISSN: 1664-235X</identifier><identifier>DOI: 10.1007/s13324-023-00828-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Complex variables ; Diophantine equation ; Functional equations ; Mathematical analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Polynomials ; Transcendental functions</subject><ispartof>Analysis and mathematical physics, 2023, Vol.13 (5)</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-p157t-39605373fb0d8eb9b0f38b27f41feba2b89d9912d976a9ea7171c4caff58e7023</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s13324-023-00828-4$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s13324-023-00828-4$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ahamed, Molla Basir</creatorcontrib><creatorcontrib>Allu, Vasudevarao</creatorcontrib><title>Transcendental solutions of Fermat-type functional equations in Cn</title><title>Analysis and mathematical physics</title><addtitle>Anal.Math.Phys</addtitle><description>The equation
f
n
+
g
n
=
1
can be interpreted as the Fermat Diophantine equation
x
n
+
y
n
=
1
within the function field when
n
is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polynomial coefficients in
C
n
. If the coefficients of the equation are transcendental functions and satisfy a certain relationship, we show that transcendental solutions can be obtained. Moreover, we determine the precise form of the solutions in both cases.</description><subject>Analysis</subject><subject>Complex variables</subject><subject>Diophantine equation</subject><subject>Functional equations</subject><subject>Mathematical analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Polynomials</subject><subject>Transcendental functions</subject><issn>1664-2368</issn><issn>1664-235X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNpFkE1LxDAQhoMouKz7BzwVPEdnkjQfRy2uCgteVvAW0jaRLjXtNu3Bf2_Xip7mhXl4mXkIuUa4RQB1l5BzJigwTgE001SckRVKKSjj-fv5X5b6kmxSOgAAilwKqVbkYT-4mCofax9H12apa6ex6WLKupBt_fDpRjp-9T4LU6xOi5nxx8ktTBOzIl6Ri-Da5De_c03eto_74pnuXp9eivsd7TFXI-VGQs4VDyXU2pemhMB1yVQQGHzpWKlNbQyy2ijpjHcKFVaiciHk2qv5uTW5WXr7oTtOPo320E3DfFCyTAs0CnOGM8UXKvVDEz_88E8h2JMvu_iyc6X98WUF_waKSF24</recordid><startdate>2023</startdate><enddate>2023</enddate><creator>Ahamed, Molla Basir</creator><creator>Allu, Vasudevarao</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope/></search><sort><creationdate>2023</creationdate><title>Transcendental solutions of Fermat-type functional equations in Cn</title><author>Ahamed, Molla Basir ; Allu, Vasudevarao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-39605373fb0d8eb9b0f38b27f41feba2b89d9912d976a9ea7171c4caff58e7023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Complex variables</topic><topic>Diophantine equation</topic><topic>Functional equations</topic><topic>Mathematical analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Polynomials</topic><topic>Transcendental functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ahamed, Molla Basir</creatorcontrib><creatorcontrib>Allu, Vasudevarao</creatorcontrib><jtitle>Analysis and mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ahamed, Molla Basir</au><au>Allu, Vasudevarao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Transcendental solutions of Fermat-type functional equations in Cn</atitle><jtitle>Analysis and mathematical physics</jtitle><stitle>Anal.Math.Phys</stitle><date>2023</date><risdate>2023</risdate><volume>13</volume><issue>5</issue><issn>1664-2368</issn><eissn>1664-235X</eissn><abstract>The equation
f
n
+
g
n
=
1
can be interpreted as the Fermat Diophantine equation
x
n
+
y
n
=
1
within the function field when
n
is a positive integer. This study employs Nevanlinna theory for several complex variables to explore transcendental solutions of Fermat-type functional equations with polynomial coefficients in
C
n
. If the coefficients of the equation are transcendental functions and satisfy a certain relationship, we show that transcendental solutions can be obtained. Moreover, we determine the precise form of the solutions in both cases.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s13324-023-00828-4</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1664-2368 |
| ispartof | Analysis and mathematical physics, 2023, Vol.13 (5) |
| issn | 1664-2368 1664-235X |
| language | eng |
| recordid | cdi_proquest_journals_2841971521 |
| source | SpringerNature Journals |
| subjects | Analysis Complex variables Diophantine equation Functional equations Mathematical analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Polynomials Transcendental functions |
| title | Transcendental solutions of Fermat-type functional equations in Cn |
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