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