You are cordially invited to the Number Theory Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Tomos Parry (Bilkent)<\/p>\n
\u201cSummation formulas in analytic number theory\u201d<\/p>\n
Abstract: Let \u03c0(x) be the number of primes up to x. If you want to count primes then you can write the count as an integral in the complex plane<\/p>\n
x \u03c0()=\u222b_(2-i\u221e)^(2+i\u221e)\u2592\u3016P(s) x^s\/s ds\u3017 where P(s)=\u2211_p\u25921\/p^s<\/p>\n
Analysing the complex analytic properties on the RHS then lets you say something about the arithmetic problem on the LHS \u2013 this is the classical proof of the Prime Number Theorem.<\/p>\n
This seminar is the second of 5-6 seminars in this mini seminar series. Last week we showed how the above is an example of Mellin inversion and this week we\u2019ll prove the above formula, apply it in the case of the divisor function, and show how it leads to Voronoi\u2019s summation formula. This talk will be more involved than the more \u201coverview\u201d style of the last talk, to which we\u2019ll return next week.<\/p>\n
Date: Friday, Feb 28, 2025
\nTime: 19:00
\nPlace: SB-Z11<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the Number Theory Seminar organized by the Department of Mathematics. Speaker: Tomos Parry (Bilkent) \u201cSummation formulas in analytic number theory\u201d Abstract: Let \u03c0(x) be the number of primes up to x. If you want to count primes then you can write the count as an [\u2026] <\/p>\n