You are cordially invited to the Number Theory Seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Tomos Parry (Bilkent)<\/p>\n
“Summation formulas in analytic number theory”<\/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
\u03c0(x)= \u222b_(2-i\u221e)^(2+i\u221e)\u2592\u3016P(s) x^s\/s ds\u3017<\/p>\n
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 – this is the classical proof of the Prime Number Theorem.<\/p>\n
The above formula is known as Perron’s formula and is really an example of a Mellin inversion. In this mini seminar series we’ll discuss the formula in this Mellin inversion context and discuss further formulas exemplifying this, especially Voronoi’s summation formula.<\/p>\n
The nature of the talks will be informal and the discussion of Perron and Mellin inversion will be more of an overview rather than details, lasting 2-3 talks. This part should give an idea of what analytic number theory looks like from afar – in particular the hope is it can appeal to undergraduates if they know some complex analysis. In the 2-3 talks after we’ll see what it looks like up close by doing Voronoi in more detail.<\/p>\n
Date: Friday, Feb 21, 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) “Summation formulas in analytic number theory” 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