{"id":152,"date":"2018-05-10T10:56:14","date_gmt":"2018-05-10T10:56:14","guid":{"rendered":"http:\/\/blog.metu.edu.tr\/komer\/?page_id=152"},"modified":"2025-02-04T08:19:17","modified_gmt":"2025-02-04T08:19:17","slug":"research","status":"publish","type":"page","link":"https:\/\/blog.metu.edu.tr\/komer\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

My main area of study is algebraic number theory. I am interested in elliptic curves and complex multiplication. My thesis concerns the class numbers of ray class fields of imaginary quadratic fields. I am currently focused on arithmetically exceptional mappings and generalized Chebyshev polynomials associated with Lie algebras.<\/p>\n

Curriculum Vitae<\/a> (updated January 2025)<\/p>\n

Publications<\/h2>\n

Note that the actual published versions may be slightly different than the versions given below.
\n\n\n\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
14<\/td>On the Jacobian Matrices of Generalized Chebyshev Polynomials<\/a>,<\/br> J. of Lie Theory, Vol. 35, (2025), 1-16.
\nJoint with A. \u0130leri.<\/td>\n<\/tr>\n
13<\/td>Value sets of folding polynomials over finite fields<\/a>,
\nTurk. J. Math., 43, (2019), 1407-1413.<\/td>\n<\/tr>\n
12<\/td>A proof of the Lucas-Lehmer test and its variations by using a singular cubic curve<\/a>,
\nJournal of Integer Sequences, 21, (2018), Article 18.6.2.<\/td>\n<\/tr>\n
11<\/td>Value sets of bivariate folding polynomials over finite fields<\/a>,
\nFinite Fields Appl., 54, (2018), 253-272.<\/td>\n<\/tr>\n
10<\/td>On the Arithmetic Exceptionality of Polynomial Mappings<\/a>,
\nBull. London Math. Soc., 50, (2018), 143-147.<\/td>\n<\/tr>\n
9<\/td>Arithmetic Exceptionality of Generalized Latt\u00e8s Maps<\/a>,
\nJ. Math. Soc. Japan 70 No.2 (2018) 823-832.
\nJoint with H. \u00d6nsiper<\/a>.<\/td>\n<\/tr>\n
8<\/td>Bivariate polynomial mappings associated with simple complex Lie algebras<\/a>,
\nJ. Number Theory, 168, (2016), 433-451.<\/td>\n<\/tr>\n
7<\/td>Value sets of bivariate Chebyshev maps over finite fields<\/a>,
\nFinite Fields Appl., 36, (2015), 189-202.<\/td>\n<\/tr>\n
6<\/td>On the computation of generalized division polynomials<\/a>,
\nTurk. J. Math., 39, (2015), 547-555.<\/td>\n<\/tr>\n
5<\/td>On the units generated by Weierstrass forms<\/a>,
\nANTS 2014 proceeding,
\nLMS J. Comput. Math., 17 (2014), suppl. A, 303-313.<\/td>\n<\/tr>\n
4<\/td>Value sets of Latt\u00e8s maps over finite fields<\/a>,
\nJ. Number Theory, 143, (2014), 262-278.<\/td>\n<\/tr>\n
3<\/td>A recurrence relation for Bernoulli numbers<\/a>,
\nHacet. J. Math. Stat., 42, (2013), no 4, 319-329.<\/td>\n<\/tr>\n
2<\/td>Class numbers of ring class fields of prime conductor<\/a>,
\nActa Arith., 153, (2012), no 3, 251-269.<\/td>\n<\/tr>\n
1<\/td>Class numbers of ray class fields of imaginary quadratic fields<\/a>,
\nMath. Comp., 80, (2011), no. 274, 1099-1122.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n","protected":false},"excerpt":{"rendered":"

My main area of study is algebraic number theory. I am interested in elliptic curves and complex multiplication. My thesis […]<\/p>\n","protected":false},"author":584,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-152","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/pages\/152","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/users\/584"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/comments?post=152"}],"version-history":[{"count":0,"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/pages\/152\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.metu.edu.tr\/komer\/wp-json\/wp\/v2\/media?parent=152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}