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Packet 2: Bonus 6

In 2024, MIT professors 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] Name these values, which are called “trivial” when 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: zeros of the Riemann zeta function [accept roots of the Riemann zeta function; prompt on roots 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

HeardPPBE %M %H %
3319.3994%61%39%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
EdinburghManchester B10101030HME
Manchester ASheffield A001010E
Sheffield BChimera001010E

Summary

TournamentEditionMatchHeardPPBE %M %H %
VAULT II at Georgia Tech2026-01-24✓623.33100%83%50%
Triangle Cup2026-03-13✓316.6767%67%33%
VAULT II at Eden Prairie HS2026-03-13✓220.00100%50%50%
VAULT II at McGill2026-03-13✓417.50100%50%25%
VAULT II at UCSB2026-03-13✓225.00100%100%50%
VAULT II Northern UK2026-04-24✓316.67100%33%33%
VAULT II Southern UK2026-04-24✓417.50100%50%25%
VAULT II at Harvard2026-04-30✓425.00100%100%50%
VAULT II at MINT2026-06-19✓514.0080%20%40%
VAULT II Stanford Online2026-07-17✕825.00100%75%75%