{"id":1156,"date":"2013-03-15T11:35:21","date_gmt":"2013-03-15T02:35:21","guid":{"rendered":"http:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/?p=1156"},"modified":"2013-03-15T13:57:53","modified_gmt":"2013-03-15T04:57:53","slug":"20130329","status":"publish","type":"post","link":"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20130329\/","title":{"rendered":"Mitsugu Hirasaka, Zeta functions of adjacecny algebras"},"content":{"rendered":"<div class=\"talk\">Zeta functions of adjacecny algebras<\/div>\n<div class=\"speaker\"><a href=\"http:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/entry\/20130329\/\">Mitsugu Hirasaka<\/a><br \/>\nDepartment of Mathematics,Pusan National University<\/div>\n<div class=\"date\">2013\/03\/29 Fri 4PM-5PM<\/div>\n<div class=\"abstract\">\nFor a module <i>L<\/i> the formal Dirichlet series <MATH>&zeta;<sub><i>L<\/i><\/sub><i>(s)<\/i> = &sum;<sub><i>n<\/i> &ge; 1<\/i><\/sub><i>a<sub>n<\/sub>n<sup>-s<\/sup><\/i><\/MATH> is defined whenever the number <i>a<sub>n<\/sub><\/i> of submodules of <i>L<\/i> with index <i>n<\/i> is finite for each positive integer <i>n<\/i>. For a ring <i>R<\/i> and a finite association scheme <i>(X,S)<\/i> we denote the adjacency algebra of <i>(X,S)<\/i> over <i>R<\/i> by <i>RS<\/i>. In this talk we aim to compute <MATH>&zeta;<sub><b>Z<\/b>S<\/sub>(s)<\/MATH> where <MATH><b>Z<\/b>S<\/MATH> is regarded as a <MATH><b>Z<\/b>S<\/MATH>-module under the assumption that <MATH>|X|<\/MATH> is prime or <MATH>|S|=2<\/MATH>.<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Zeta functions of adjacecny algebras Mitsugu Hirasaka Department of Mathematics,Pusan National University 2013\/03\/29 Fri 4PM-5PM For a module L the formal Dirichlet series &zeta;L(s) = &sum;n &ge; 1ann-s is defined whenever the number an of submodules of L with index n is finite for each positive integer n. For a ring R and a finite [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_newsletter_tier_id":0,"jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[111,17],"tags":[35],"jetpack_publicize_connections":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mitsugu Hirasaka, Zeta functions of adjacecny algebras - KAIST Discrete Math Seminar<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20130329\/\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"andreash\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20130329\/\",\"url\":\"https:\/\/mathsci.kaist.ac.kr\/~sangil\/seminar\/20130329\/\",\"name\":\"Mitsugu Hirasaka, Zeta functions of adjacecny algebras - 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