{"id":24179,"date":"2025-03-20T17:34:49","date_gmt":"2025-03-20T14:34:49","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?p=24179"},"modified":"2025-03-23T20:46:36","modified_gmt":"2025-03-23T17:46:36","slug":"math-seminar-voronois-summation-formula-tomos-parry-730pm-march-21-2025-en","status":"publish","type":"post","link":"https:\/\/w3.bilkent.edu.tr\/en\/math-seminar-voronois-summation-formula-tomos-parry-730pm-march-21-2025-en\/","title":{"rendered":"MATH Seminar: \u201cVoronoi\u2019s Summation Formula\u201d, Tomos Parry, 7:30PM March 21 2025 (EN)"},"content":{"rendered":"

You are cordially invited to the Number Theory Seminar organized by the Department of Mathematics.<\/p>\n

\u201cVoronoi\u2019s summation formula\u201d<\/p>\n

Speaker: Tomos Parry (Bilkent)<\/p>\n

Abstract: The divisor function<\/p>\n

d(n):=# divisors of n<\/p>\n

is one of the most studied sequences in number theory. This is the fourth seminar about d(n) in a mini-series, where so far we have:<\/p>\n

    \n
  1. Discussed Perron\u2019s formula \u2013 a contour integral expression for whatever we\u2019re counting. This is the starting point of studying a sequence through the analytic properties of a series associated to the sequence (its Dirichlet series). This let us approximate the average of d(n) up to an error \u221ax (which is no better than an elementary argument though).<\/li>\n
  2. Analysed the integrals in Perron\u2019s formula more carefully \u2013 improving the error to x^(1\/3), which is now considerably better than elementary.<\/li>\n
  3. Kept the integrals explicit and wrote the error as a sum of these terms \u2013 this is Voronoi\u2019s summation formula.<\/li>\n<\/ol>\n

    This week is 4. Repeat the above analysis but with a smoothing weight \u2013 this shows us that the integral analysis wasn\u2019t really the \u201cimportant part\u201d of the above arguments, rather just Mellin inversion and continuation of the Dirichlet series.<\/p>\n

    Date: Friday, March 21, 2025
    \nTime: 19:30
    \nPlace: SB-Z11<\/p>\n","protected":false},"excerpt":{"rendered":"

    You are cordially invited to the Number Theory Seminar organized by the Department of Mathematics. \u201cVoronoi\u2019s summation formula\u201d Speaker: Tomos Parry (Bilkent) Abstract: The divisor function d(n):=# divisors of n is one of the most studied sequences in number theory. This is the fourth seminar about d(n) in a mini-series, [\u2026] <\/p>\n

    <\/div>\n

    Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-24179","post","type-post","status-publish","format-standard","hentry","category-oldposts"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/posts\/24179","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/comments?post=24179"}],"version-history":[{"count":1,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/posts\/24179\/revisions"}],"predecessor-version":[{"id":24180,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/posts\/24179\/revisions\/24180"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=24179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/categories?post=24179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/tags?post=24179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}