- 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) Carl Friedrich Gauss
B) Bernhard Riemann
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) Riemann Hypothesis
B) Collatz Conjecture
C) Twin Prime Conjecture
D) Goldbach Conjecture
- 4. In the Dirichlet L-function L(s, χ), what does the character χ represent?
A) Meissel–Mertens constant
B) Dirichlet character
C) Liouville function
D) Euler's constant
- 5. Which branch of number theory focuses on the properties of integers using analysis?
A) Elementary Number Theory
B) Computational Number Theory
C) Analytic Number Theory
D) Algebraic Number Theory
- 6. Who introduced the concept of the Möbius function in number theory?
A) Andrey Kolmogorov
B) August Ferdinand Möbius
C) Ernst Eduard Kummer
D) Carl Friedrich Gauss
- 7. Which famous Swiss mathematician made significant contributions to Analytic Number Theory and Mathematical Physics?
A) Georg Cantor
B) Paul Erdős
C) Leonhard Euler
D) Andrew Wiles
- 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. Which mathematical function is commonly used in Analytic Number Theory to study the distribution of primes?
A) Bessel function
B) Gamma function
C) Riemann zeta function
D) Lambert W function
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