- 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) ϑ(s)
B) Γ(s)
C) π(s)
D) ζ(s)
- 2. Which mathematician made significant contributions to Analytic Number Theory with the Prime Number Theorem?
A) Bernhard Riemann
B) Carl Friedrich Gauss
C) Pierre-Simon Laplace
D) Leonhard Euler
- 3. What is the famous unsolved problem in Analytic Number Theory related to the zeta function zeros?
A) Twin Prime Conjecture
B) Collatz Conjecture
C) Riemann Hypothesis
D) Goldbach Conjecture
- 4. In the Dirichlet L-function L(s, χ), what does the character χ represent?
A) Liouville function
B) Euler's constant
C) Meissel–Mertens constant
D) Dirichlet character
- 5. Which branch of number theory focuses on the properties of integers using analysis?
A) Analytic Number Theory
B) Computational Number Theory
C) Algebraic Number Theory
D) Elementary Number Theory
- 6. Which mathematical function is commonly used in Analytic Number Theory to study the distribution of primes?
A) Gamma function
B) Riemann zeta function
C) Bessel function
D) Lambert W function
- 7. Which famous Swiss mathematician made significant contributions to Analytic Number Theory and Mathematical Physics?
A) Georg Cantor
B) Paul Erdős
C) Andrew Wiles
D) Leonhard Euler
- 8. What is the central question addressed by Analytic Number Theory?
A) Existence of irrational numbers
B) Proof of Goldbach Conjecture
C) Convergence of infinite series
D) Distribution of prime numbers
- 9. Who introduced the concept of the Möbius function in number theory?
A) August Ferdinand Möbius
B) Andrey Kolmogorov
C) Carl Friedrich Gauss
D) Ernst Eduard Kummer
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