{"id":800,"date":"2019-05-02T10:36:30","date_gmt":"2019-05-02T01:36:30","guid":{"rendered":"http:\/\/mathematicians.korea.ac.kr\/sk23\/?p=800"},"modified":"2019-05-02T10:36:50","modified_gmt":"2019-05-02T01:36:50","slug":"800","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/sk23\/2019\/05\/02\/800\/","title":{"rendered":"Zero density estimates of an Epstein zeta function"},"content":{"rendered":"<p>\ub300\uc218\ud559 \uc138\ubbf8\ub098\uc785\ub2c8\ub2e4. <\/p>\n<p>\uc81c\ubaa9: Zero density estimates of an Epstein zeta function near the half line<br \/>\n\uc5f0\uc0ac: \uc774\uc724\ubcf5 (\uc778\ucc9c\ub300\ud559\uad50)<br \/>\n\uc77c\uc2dc: 2019\ub144 5\uc6d4 2\uc77c \ubaa9\uc694\uc77c, 15:00-16:00<br \/>\n\uc7a5\uc18c: \uc544\uc0b0\uc774\ud559\uad00 526\ud638 <\/p>\n<p>Abstract: Let Q be a positive definite quadratic form with integral coefficients and let E(s,Q) be the Epstein zeta function associated with Q. Assume that the class number of Q is bigger than 1. Then we estimate the number of zeros of E(s,Q) in the region Re(s) &gt; \\sigma_T (\\theta) := 1\/2 + (\\log T)^{-\\theta} and T &lt; Im(s) &lt; 2T, to provide its asymptotic formula for fixed 0 &lt; \\theta &lt; 1 conditionally. Moreover, it is unconditional if the class number of Q is 2 or 3 and 0 &lt; \\theta &lt; 1\/13.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ub300\uc218\ud559 \uc138\ubbf8\ub098\uc785\ub2c8\ub2e4. \uc81c\ubaa9: Zero density estimates of an Epstein zeta function near the half line \uc5f0\uc0ac: \uc774\uc724\ubcf5 (\uc778\ucc9c\ub300\ud559\uad50) \uc77c\uc2dc: 2019\ub144 5\uc6d4 2\uc77c \ubaa9\uc694\uc77c, 15:00-16:00 \uc7a5\uc18c: \uc544\uc0b0\uc774\ud559\uad00 526\ud638 Abstract: Let Q be a positive definite quadratic form with integral coefficients and let E(s,Q) be the Epstein zeta function associated with Q. Assume that the class number &#8230; <a title=\"Zero density estimates of an Epstein zeta function\" class=\"read-more\" href=\"https:\/\/mathematicians.korea.ac.kr\/sk23\/2019\/05\/02\/800\/\" aria-label=\"Zero density estimates of an Epstein zeta function\uc5d0 \ub300\ud574 \ub354 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uc138\uc694\">\ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-800","post","type-post","status-publish","format-standard","hentry","category-news-events"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/sk23","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/800","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/comments?post=800"}],"version-history":[{"count":2,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/800\/revisions"}],"predecessor-version":[{"id":802,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/posts\/800\/revisions\/802"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/media?parent=800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/categories?post=800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/sk23\/wp-json\/wp\/v2\/tags?post=800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}