BEGIN:VCALENDAR
VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Number Theory Seminar
X-WR-TIMEZONE:Central Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260916T210744Z
UID:tag:localist.com\,2008:EventInstance_51207621488918
DTSTART:20251112T203000Z
DTEND:20251112T212000Z
DESCRIPTION:Speaker: COL John Dvorak  ( Army University at Fort Leavenworth
  )\n\n \n\nTitle: Prime-Based Corrections to Riemann Zero Counting via Tru
 ncated Euler Products\n\nAbstract: The Riemann explicit formula expresses 
 prime counting functions as sums over zeta zeros\, a cornerstone of analyt
 ic number theory since 1859. We demonstrate the computational viability of
  the reverse direction: using primes to approximate $S(T) = (1/\\pi)\\arg\
 \zeta(1/2+iT)$\, the oscillatory correction term in the zero counting func
 tion $N(T)$\, via truncated Euler products. The Euler product expansion yi
 elds $S(T) = -(1/\\pi)\\sum_p \\sum_{k=1}^{\\infty} (1/k) p^{-k/2} \\sin(k
 T\\log p)$\, which diverges on the critical line but exhibits slow heurist
 ic divergence $\\sim \\sqrt{\\log\\log P_{\\max}}$ under random-phase canc
 ellation\, enabling optimal finite truncation.  Performance is highly hete
 rogeneous: 41\\% of test heights require only 1\,000 primes for substantia
 l improvement (``ultra-easy'')\, while 7\\% exhibit catastrophic failure r
 egardless of truncation. We introduce a three-factor logistic regression m
 odel (proximity to zeros\, signal amplitude $|S(T)|$\, and truncation para
 meter) to account for these performance disparities.  This work provides a
  novel large-scale empirical validation of computational prime-zero dualit
 y\, complementing Gonek's theoretical conditions and LeClair's ultra-high 
 zero computations with systematic performance quantification and practical
  guidelines.
LOCATION:
SUMMARY:Number Theory Seminar
URL;VALUE=URI:https://events.k-state.edu/event/number-theory-seminar-630
CATEGORIES:Lecture\, Colloquia\, Seminar
END:VEVENT
END:VCALENDAR