{"id":24866,"date":"2025-05-26T16:19:18","date_gmt":"2025-05-26T13:19:18","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?p=24866"},"modified":"2025-05-30T22:59:07","modified_gmt":"2025-05-30T19:59:07","slug":"math-seminar-selbergs-sieve-tomos-parry-700pm-may-30-2025-en","status":"publish","type":"post","link":"https:\/\/w3.bilkent.edu.tr\/en\/math-seminar-selbergs-sieve-tomos-parry-700pm-may-30-2025-en\/","title":{"rendered":"MATH Seminar: \u201cSelberg\u2019s sieve\u201d, Tomos Parry, 7:00PM May 30 2025 (EN)"},"content":{"rendered":"

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

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

\u201d Selberg\u2019s sieve\u201d<\/p>\n

Abstract: A sieve picks out the numbers left over after removing multiples of certain primes, using an indicator function like<\/p>\n

                                                \u2211_(d|n)\u2592\u3016\u03bc(d)\u3017={\u2588(1  for  n=1@0 for & n>1.)\u2524\r\n<\/code><\/pre>\n
If we are prepared to accept upper bounds instead of equality, then Selberg\u2019s observation is that we can replace the above with<\/p>\n
(\u2211_(d|n)\u2592\u03b3(d) )^2\u2265{\u2588(1 for n=1@0 for n=0)\u2524<\/p>\n
where \u03b3(d) is any value we want as long as \u03b3(1)=1.<\/p>\n
The simplicity of this\u00a0a square is positive\" bound therefore gives us a lot of freedom in choosing \u03b3(d). This gives results as strong as the earlier (<\/code>combinatorial\u201d) sieves.<\/p>\n
Date: Friday, May 30, 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) \u201d Selberg\u2019s sieve\u201d Abstract: A sieve picks out the numbers left over after removing multiples of certain primes, using an indicator function like \u2211_(d|n)\u2592\u3016\u03bc(d)\u3017={\u2588(1 for n=1@0 for & n>1.)\u2524 If we [\u2026] <\/p>\n
<\/div>\n
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