Packet 2: Bonus 6
In 2024, Larry Guth and James Maynard proved a new upper bound on the number of these values between 0.75 and 1. For 10 points each:
[10h] What values are called “trivial” when they are equal to a negative even integer? An unsolved conjecture claims that all “nontrival” types of these values have a real part of “one half.”
ANSWER: non-trivial zeroes of the Riemann zeta function [accept roots or solutions of the Riemann zeta function; prompt on roots or solutions or zeros alone]
[10m] When evaluated at 1, the Riemann zeta function is equal to this series. The Euler-Mascheroni constant is defined as the limiting difference between this series and the natural log.
ANSWER: harmonic series
[10e] In 1737, Euler proved that for real inputs, the Riemann zeta function is equal to the infinite product of “1 over 1 - [these numbers] to the s.” These numbers are only divisible by 1 and themselves.
ANSWER: primes
<Science - Math, Omkar Marathe> | VAULT II Packet 02
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 8 | 25.00 | 100% | 75% | 75% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Armand duplantis fan club | Michael Touse-Squid | 10 | 10 | 10 | 30 | HME |
| Booz Allen Interns | Jeopardy Rejected Ibean Batutu | 10 | 10 | 10 | 30 | HME |
| Mountain Dew is Better | Virginia Tech | 0 | 0 | 10 | 10 | E |
| Not Just Biking | They fuck you up your buzz and neg | 10 | 10 | 10 | 30 | HME |
| Ostia Orcas | An even worse idea | 10 | 10 | 10 | 30 | HME |
| PC Chris Master Race | I have no buzzer and I must neg | 10 | 10 | 10 | 30 | HME |
| The Young Jits | Ted Offensive | 10 | 10 | 10 | 30 | HME |
| They'll Just Let Anyone Edit Chicago Open These Days | Hoya gonna stop the Fighting Irish? | 0 | 0 | 10 | 10 | E |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| VAULT II at Georgia Tech | 2026-01-24 | ✕ | 6 | 23.33 | 100% | 83% | 50% |
| Triangle Cup | 2026-03-13 | ✕ | 3 | 16.67 | 67% | 67% | 33% |
| VAULT II at Eden Prairie HS | 2026-03-13 | ✕ | 2 | 20.00 | 100% | 50% | 50% |
| VAULT II at McGill | 2026-03-13 | ✕ | 4 | 17.50 | 100% | 50% | 25% |
| VAULT II at UCSB | 2026-03-13 | ✕ | 2 | 25.00 | 100% | 100% | 50% |
| VAULT II Northern UK | 2026-04-24 | ✕ | 3 | 16.67 | 100% | 33% | 33% |
| VAULT II Southern UK | 2026-04-24 | ✕ | 4 | 17.50 | 100% | 50% | 25% |
| VAULT II at Harvard | 2026-04-30 | ✕ | 4 | 25.00 | 100% | 100% | 50% |
| VAULT II at MINT | 2026-06-19 | ✕ | 5 | 14.00 | 80% | 20% | 40% |
| VAULT II Stanford Online | 2026-07-17 | ✓ | 8 | 25.00 | 100% | 75% | 75% |