BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Stelios Sachpazis (Université de Montréal) DTSTART:20221212T140000Z DTEND:20221212T150000Z DTSTAMP:20260423T021326Z UID:GANT/18 DESCRIPTION:Title: A different proof of Linnik's estimate for primes in arithmetic progressions \nby Stelios Sachpazis (Université de Montréal) as part of Greek Alg ebra & Number Theory Seminar\n\n\nAbstract\nLet $a$ and $q$ be two coprime positive integers. In 1944\, Linnik\nproved his celebrated theorem concer ning the size of the smallest prime\n$p(q\,a)$ in the arithmetic progressi on $a(\\mod q)$. In his attempt to prove\nhis result\, Linnik established an estimate for the sums of the von Mangoldt\nfunction $\\Lambda$ on arith metic progressions. His work on $p(q\,a)$ was later\nsimplified\, but the simplified proofs relied in one form or another on the\nsame advanced tool s that Linnik originally used. The last two decades\, some\nmore elementar y approaches for Linnik's theorem have appeared. Nonetheless\,\nnone of th em furnishes an estimate of the same quantitative strength as the\none tha t Linnik obtained for $\\Lambda$. In this talk\, we will see how one can s eal\nthis gap and recover Linnik’s estimate by largely elementary means. The\nideas that I will describe build on methods from the treatment of\nK oukoulopoulos on multiplicative functions with small partial sums and his\ npretentious proof for the prime number theorem in arithmetic progressions .\n LOCATION:https://researchseminars.org/talk/GANT/18/ END:VEVENT END:VCALENDAR