{"id":432,"date":"2009-12-14T15:48:10","date_gmt":"2009-12-14T19:48:10","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=432"},"modified":"2009-12-14T15:48:10","modified_gmt":"2009-12-14T19:48:10","slug":"prove-my-lemma-get-acknowledged-in-a-paper","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=432","title":{"rendered":"Prove my lemma, get acknowledged in a paper!"},"content":{"rendered":"<p>This will be a little experiment, in which the <a href=\"http:\/\/gowers.wordpress.com\/2009\/01\/27\/is-massively-collaborative-mathematics-possible\/\">collaborative mathematics<\/a> advocated by Timothy Gowers and others combines with my own frustration and laziness.\u00a0 If it goes well, I might try it more in the future.<\/p>\n<p>Let p be a complex polynomial of degree d.\u00a0 Suppose that |p(z)|\u22641 for all z such that |z|=1 and |z-1|\u2265\u03b4 (for some small \u03b4&gt;0).\u00a0 Then what&#8217;s the best upper bound you can prove on |p(1)|?<\/p>\n<p><strong>Note:<\/strong> I can prove an upper bound of the form |p(1)|\u2264exp(\u03b4d)&#8212;indeed, that holds even if p can be a polynomial in both z and its complex conjugate (and is tight in that case).\u00a0 What <em>really<\/em> interests me is whether a bound of the form |p(1)|\u2264exp(\u03b4<sup>2<\/sup>d) is true.<\/p>\n<p><input id=\"gwProxy\" type=\"hidden\" \/><!--Session data--><strong>Update:<\/strong> After I accepted Scott Morrison&#8217;s suggestion to post my problem at <a href=\"http:\/\/mathoverflow.net\/\">mathoverflow.net<\/a>, the problem was <a href=\"http:\/\/mathoverflow.net\/questions\/8912\/analogue-of-the-chebyshev-polynomials-over-c\/8915#8915\">solved<\/a> 11 minutes later by David Speyer, using a very nice reduction to the case I&#8217;d already solved.\u00a0 Maybe I should feel sheepish, but I don&#8217;t&#8212;I feel grateful.\u00a0 I am now officially a fan of mathoverflow.\u00a0 Go there and participate! <input onclick=\"jsCall();\" id=\"jsProxy\" type=\"hidden\" \/> <input id=\"gwProxy\" type=\"hidden\" \/><!--Session data--><br \/>\n<input onclick=\"jsCall();\" id=\"jsProxy\" type=\"hidden\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This will be a little experiment, in which the collaborative mathematics advocated by Timothy Gowers and others combines with my own frustration and laziness.\u00a0 If it goes well, I might try it more in the future. Let p be a complex polynomial of degree d.\u00a0 Suppose that |p(z)|\u22641 for all z such that |z|=1 and [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[5],"tags":[],"class_list":["post-432","post","type-post","status-publish","format-standard","hentry","category-complexity"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/432","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=432"}],"version-history":[{"count":0,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/432\/revisions"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}