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BEGIN:VEVENT
UID:c4f21096139b24964b0cab04abfaf5b5
CATEGORIES:Number Theory Seminar
CREATED:20221009T180833
SUMMARY:The least Euler prime via sieve
LOCATION:Hill Center 425 and zoom
DESCRIPTION:<p style="background: white;"><strong>Abstract:&nbsp;</strong>Euler primes 
 are primes of the form $p = x^2+Dy^2$ with $D&gt;0$. In analogy with Linnik
 's theorem, we can ask if it is possible to show that $p(D)$, the least pri
 me of this form, satisfies $p(D) ll D^A$ for some constant $A&gt;0$. Indeed
  Weiss showed this in 1983, but it wasn't until 2016 that an explicit value
  for $A$ was determined by Thorner and Zaman, who showed one can take $A=69
 4$. Their work follows the same outline as the traditional approach to prov
 ing Linnik's theorem, relying on log-free zero-density estimates for Hecke 
 L-functions and a quantitative Deuring-Heilbronn phenomenon. In an ongoing 
 work (as part of my PhD thesis) we propose an alternative approach to the p
 roblem via sieve methods that avoids the use of the above technical results
  on zeros of the Hecke L-functions. We hope that such simplifications may r
 esult in a better value for the exponent $A$.</p>
CONTACT:Louis Gaudet (Rutgers)
X-EXTRAINFO:Join Zoom Meeting https://rutgers.zoom.us/j/96537865394?pwd=NUh0SzAwd0RIYkZ
 DM21OSFgrRHVVZz09 \nJoin by SIP RegularLabs.EmailProtector.unCloak("ep_15cd
 a5ab"); \nMeeting ID: 965 3786 5394 \nPassword: Riemann
DTSTAMP:20260829T131538
DTSTART;TZID=America/New_York:20221011T140000
DTEND;TZID=America/New_York:20221011T150000
SEQUENCE:0
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