BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20211107T010000 RDATE:20220313T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20221106T010000 RDATE:20230312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20231105T010000 RDATE:20240310T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20211010T140000 RDATE:20211107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20220313T030000 RDATE:20221106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20230312T030000 RDATE:20231105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20240310T030000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:c4f21096139b24964b0cab04abfaf5b5 CATEGORIES:Number Theory Seminar CREATED:20221009T180833 SUMMARY:The least Euler prime via sieve LOCATION:Hill Center 425 and zoom DESCRIPTION:Abstract: Euler primes are primes of the form $p = x^2+Dy^2$ with $D>0$. In analogy with Linnik's theorem, we can ask if it is possible to show tha t $p(D)$, the least prime of this form, satisfies $p(D) ll D^A$ for some co nstant $A>0$. 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 sh owed one can take $A=694$. Their work follows the same outline as the tradi tional approach to proving Linnik's theorem, relying on log-free zero-densi ty estimates for Hecke L-functions and a quantitative Deuring-Heilbronn phe nomenon. In an ongoing work (as part of my PhD thesis) we propose an altern ative approach to the problem via sieve methods that avoids the use of the above technical results on zeros of the Hecke L-functions. We hope that suc h simplifications may result in a better value for the exponent $A$.\n X-ALT-DESC;FMTTYPE=text/html:

Abstract: Euler primes are primes of the form $p = x^2+Dy^2$ with $D>0$. 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 $A>0$. 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 $A$.

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_8fc4 f604"); \nMeeting ID: 965 3786 5394 \nPassword: Riemann DTSTAMP:20260830T034733 DTSTART;TZID=America/New_York:20221011T140000 DTEND;TZID=America/New_York:20221011T150000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR