{"id":18495,"date":"2023-11-14T11:18:35","date_gmt":"2023-11-14T03:18:35","guid":{"rendered":"https:\/\/cantor.math.ntnu.edu.tw\/?p=18495"},"modified":"2023-11-14T11:18:35","modified_gmt":"2023-11-14T03:18:35","slug":"1121124speech","status":"publish","type":"post","link":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/2023\/11\/14\/1121124speech\/","title":{"rendered":"[NTNU Number Theory Seminar] <\/span>\u301011\u670824\u65e5\u3011\u4e8e\u9756 \/ Quasi-periods, and the Chowla-Selberg Phenomenon"},"content":{"rendered":"\t\t
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Quasi-periods, and the Chowla-Selberg Phenomenon<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\u6642\u3000\u9593\uff1a2023-11-24 13:30 (\u4e94) \/ \u5730\u3000\u9ede\uff1aM310\u00a0<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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\u4e8e\u9756 \u9662\u58eb<\/div>
\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u540d\u8b7d\u6559\u6388<\/strong><\/div>
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I will tell a story developed in the last three decades. Chronologically this is what happens. 1987, starting from the Carlitz module with complex multiplications, Deligne, Yu, Anderson, and Gekeler discovered the quasi-periods theory for Drinfeld modules. Yu also showed the\u00a0transcendence of the non-zero quasi-periods for all the Drinfeld modules . In the meantime,\u00a0Thakur developed the gamma functions for the rational function fields in finite characteristic,\u00a0arithmetic gamma (following Goss) as well as geometric gamma.\u00a0In the 1991 Annals paper, Thakur worked out a formula for the Carlitz module with CM,\u00a0connecting its periods to special arithmetic gamma values. Developments in 1990’s by Yu,\u00a0Thakur, Sinha, Brownawell, Papanikolas proved all “special” gamma values in the function field world are transcendental. Thakur was led to conjecture\/recipes asking for formulas
expressing abelian CM periods in terms of appropriate special gamma values, i.e. the\u00a0Chowla-Selberg phenomenon.<\/p>

2004, Anderson, Brownawell, and Papanikolas determined all the algebraic relations among\u00a0special geometric gamma values (the Lang-Rohrlich conjecture). 2010, Chang, Papanikolas,\u00a0Thakur, and Yu determined all the algebraic relations among special arithmetic gamma\u00a0values. They also exhibit a Chowla-Selberg phenomenon for specific basis of quasi-periods\u00a0of Carlitz modules with CM, and verified that the transcendence degree of the field generated\u00a0by all quasi-periods equals to the rank, with canonical transcendence( also linear) basis given\u00a0by explicit special arithmetic gamma values.<\/p>

2011-12, Chang and Papanikolas prove that the analogue of the Legendre’s relation gives rise\u00a0to the only algebraic relations among quasi-periods apart from the possible complex\u00a0multiplications. For all CM Drinfeld modules, fields generated by quasi-periods always have\u00a0transcendence degree equal to the rank. 2022, Brownawell, Chang, Papanikolas, and Wei developed a complete period symbol theory in the function field setting. They prove in\u00a0particular the analogue of Shimura’s algebraic independence conjecture.\u00a0Finally in 2022, Wei verifies a strong Chowla-Selberg phenomenon for all Abelian CM\u00a0Drinfeld modules, giving an explicit linear as well as transcendence basis of quasi-periods for\u00a0any such Drinfeld module in terms of “appropriate” product of special gamma values. Appropriateness here means that the arithmetic invariants of the CM field in question are\u00a0contained in the recipe for taking product.<\/p>

In this talk we shall look closely at the fascinating connections between periods and special\u00a0Gamma values. These connections are explained by Arithmetic Geometry (algebraic number\u00a0theory together with algebraic geometry). Particularly we focus on the route from explicit\u00a0class field theory of Kronecker-Weber to the Complex Multiplication period symbol of\u00a0Shimura.<\/p>

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Speaker:\u00a0<\/strong>\u00a0\u00a0\u4e8e\u9756\u00a0<\/strong>\u00a0<\/strong>\u9662\u58eb\u00a0<\/strong>\u00a0<\/strong><\/p>

(\u570b\u7acb\u81fa\u7063\u5927\u5b78\u6578\u5b78\u7cfb\u540d\u8b7d\u6559\u6388\u3001\u570b\u7acb\u6e05\u83ef\u5927\u5b78\u6578\u5b78\u7cfb\u69ae\u8b7d\u8b1b\u5ea7\u6559\u6388\u3001\u570b\u7acb\u81fa\u7063\u5e2b\u7bc4\u5927\u5b78\u6578\u5b78\u7cfb\u8b1b\u5ea7\u6559\u6388)<\/strong><\/p>

Title \u00a0: <\/strong>Quasi-periods, and the Chowla-Selberg Phenomenon<\/p>

Time<\/strong>\u00a0 :\u00a0\u00a0 13:30 p.m.,\u00a0 November 24, 2023<\/p>

Place :\u00a0\u00a0 \u00a0<\/strong>M310, Math. Dept., National Taiwan Normal University<\/p>

Coordinators<\/strong>\u00a0:\u00a0 \u00a0Professor Jing Yu (NTU)<\/p>

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Professor Hua-Chieh Li (NTNU)<\/p>

\u3000\u3000\u3000\u3000\u3000\u3000\u3000 \u00a0\u00a0Professor Liang-Chung Hsia (NTNU)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Quasi-periods, and the Chowla-Selberg Phenomenon \u6642\u3000\u9593\uff1a20 […]<\/p>\n","protected":false},"author":21,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"off","ocean_gallery_id":[],"footnotes":""},"categories":[1,124],"tags":[],"class_list":["post-18495","post","type-post","status-publish","format-standard","hentry","category-news","category-speeches","entry"],"_links":{"self":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18495","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/users\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/comments?post=18495"}],"version-history":[{"count":8,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18495\/revisions"}],"predecessor-version":[{"id":18596,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/posts\/18495\/revisions\/18596"}],"wp:attachment":[{"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/media?parent=18495"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/categories?post=18495"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cantor.math.ntnu.edu.tw\/index.php\/wp-json\/wp\/v2\/tags?post=18495"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}