Question
The use of this function of n in the statement of the prime number theorem of Hadamard and de la Vallée Poussin (“duh lah vah-LAY poo-SAHN”) improves on Chebyshev’s result that the prime counting function of n is theta of this function of n. For 10 points each:
[10m] Give this function of natural number n that asymptotically equals the prime counting function, denoted pi, of n in the common statement of the prime number theorem.
ANSWER: n over log n [accept equivalents such as n divided by log n; accept “l·n” or “natural logarithm” instead of “log”]
[10h] This mathematician and Korobov independently proved the most recent significant improvement to the error term of the PNT. This mathematician proved a weaker version of the Goldbach conjecture for extremely large numbers.
ANSWER: Ivan Vinogradov [or Ivan Matveevich Vinogradov]
[10e] A proof of this conjecture would mean that the error term in the PNT is big O of x to the power of one-half plus epsilon, the best bound possible. Per this conjecture, all nontrivial zeros of a certain function have real part one-half.
ANSWER: Riemann hypothesis [prompt on Riemann]
<Arya Karthik, Other Science - Mathematics>
Summary
| 2023 Chicago Open | 08/05/2023 | Y | 4 | 15.00 | 100% | 50% | 0% |
Data
| Romanos IV Diogenes’ Macaroni Grill | Saint Peter Andre 3000 | 0 | 0 | 10 | 10 |
| Team Name Think Detail | The anti-STOON-dahl cabal (the tall Keyal et al.) | 0 | 0 | 10 | 10 |
| The Catastrophic Implosion of Packet Sub | BHSU | 10 | 0 | 10 | 20 |
| The Plague (anime)" was redirected to: "Oran High School Host Club | Curse you, Periplus the Platypus! | 10 | 0 | 10 | 20 |