Understanding Yitang Zhang's Contributions and the Riemann Hypothesis

What significant contribution did Yitang Zhang make to the twin prime conjecture?

• He disproved the existence of twin primes.

• He proved there are infinite primes differing by 2.

• He proved there are infinite primes differing by 70 million.

• He solved the twin prime conjecture completely.

What does the Riemann hypothesis claim about the non-trivial zeros of the Riemann-Zeta function?

• They lie on the line where the real part is -1.

• They lie on the line where the real part is 1/2.

• They lie on the line where the real part is 0.

• They lie on the line where the real part is 1.

What is the relationship between the Riemann-Zeta function and prime numbers?

• The function is unrelated to prime numbers.

• The function only applies to even numbers.

• The function helps understand the distribution of prime numbers.

• The function disproves the existence of prime numbers.

What are Dirichlet L-functions?

• A type of prime number.

• A generalisation of the Riemann-Zeta function with a weighting factor.

• A function that only applies to real numbers.

• A function that disproves the Riemann hypothesis.

What did Yitang Zhang prove about Siegel zeros?

• He proved they do not exist at all.

• He proved they exist on the critical line.

• He proved they do not exist in a specific thin region close to 1.

• He proved they exist in a large region.

What is the significance of finding a Siegel zero?

• It would disprove the Riemann hypothesis.

• It would have no impact on current mathematical theories.

• It would prove the existence of twin primes.

• It would confirm the Riemann hypothesis.

What is the main goal of Yitang Zhang's recent work on Siegel zeros?

• To disprove the twin prime conjecture.

• To eliminate the possibility of Siegel zeros in a specific region.

• To confirm the Riemann hypothesis.

• To prove the existence of Siegel zeros.

What is the general consensus among mathematicians about the existence of Siegel zeros?

• They are widely believed to exist.

• They are considered illusory and unlikely to exist.

• They are proven to exist.

• They are irrelevant to the Riemann hypothesis.

How does the peer review process in mathematics differ from other fields?

• It is only done by a single reviewer.

• It is faster and less detailed.

• It is slower and more thorough.

• It is not required for mathematical proofs.

What potential impact does the Riemann hypothesis have on physics?

• It confirms the theory of relativity.

• It disproves the laws of thermodynamics.

• It is related to the energy levels of heavy nuclei.

• It has no impact on physics.