- 1. Analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about integers. It focuses on understanding the distribution of prime numbers and other important number theoretic functions using complex analysis, calculus, and other tools from analysis. Topics in analytic number theory include prime number theorem, Riemann zeta function, Dirichlet L-functions, modular forms, and many others. This field plays a crucial role in various areas of mathematics, such as cryptography, coding theory, and theoretical computer science.
What is the Riemann zeta function typically denoted by?
A) ζ(s)
B) Γ(s)
C) π(s)
D) ϑ(s)
- 2. Which mathematician made significant contributions to Analytic Number Theory with the Prime Number Theorem?
A) Pierre-Simon Laplace
B) Leonhard Euler
C) Carl Friedrich Gauss
D) Bernhard Riemann
- 3. What is the famous unsolved problem in Analytic Number Theory related to the zeta function zeros?
A) Riemann Hypothesis
B) Twin Prime Conjecture
C) Goldbach Conjecture
D) Collatz Conjecture
- 4. In the Dirichlet L-function L(s, χ), what does the character χ represent?
A) Dirichlet character
B) Euler's constant
C) Meissel–Mertens constant
D) Liouville function
- 5. Which branch of number theory focuses on the properties of integers using analysis?
A) Computational Number Theory
B) Elementary Number Theory
C) Analytic Number Theory
D) Algebraic Number Theory
- 6. Which mathematical function is commonly used in Analytic Number Theory to study the distribution of primes?
A) Bessel function
B) Lambert W function
C) Gamma function
D) Riemann zeta function
- 7. Which famous Swiss mathematician made significant contributions to Analytic Number Theory and Mathematical Physics?
A) Paul Erdős
B) Andrew Wiles
C) Leonhard Euler
D) Georg Cantor
- 8. What is the central question addressed by Analytic Number Theory?
A) Convergence of infinite series
B) Proof of Goldbach Conjecture
C) Existence of irrational numbers
D) Distribution of prime numbers
- 9. Who introduced the concept of the Möbius function in number theory?
A) August Ferdinand Möbius
B) Ernst Eduard Kummer
C) Carl Friedrich Gauss
D) Andrey Kolmogorov
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