1.
Analytic number theory is a subject in ......?
Correct Answer
A. Mathematics
Explanation
Analytic number theory is a branch of mathematics that deals with the study of properties of numbers using techniques from analysis. It involves the application of analytical methods to understand the distribution of prime numbers, the behavior of arithmetic functions, and the properties of number-theoretic functions. Therefore, the correct answer is Mathematics.
2.
Analytic number theory can be split up into how many major parts?
Correct Answer
A. Two
Explanation
Analytic number theory can be split up into two major parts.
3.
Much of analytic number theory was inspired by the ........?
Correct Answer
B. Prime number theorem
Explanation
The correct answer is the Prime number theorem. Analytic number theory, which deals with the properties of integers and prime numbers using analytic methods, was greatly influenced by the Prime number theorem. This theorem provides an estimate for the distribution of prime numbers and has been a fundamental result in number theory. Its discovery and proof have led to significant advancements in the field of analytic number theory.
4.
In two papers from years ......., the Russian mathematician Pafnuty L'vovich Chebyshev attempted to prove the asymptotic law of distribution of prime numbers.
Correct Answer
D. 1848 and 1850
Explanation
In 1848 and 1850, the Russian mathematician Pafnuty L'vovich Chebyshev attempted to prove the asymptotic law of distribution of prime numbers.
5.
In two papers from 1848 and 1850, the Russian mathematician ........... attempted to prove the asymptotic law of distribution of prime numbers.
Correct Answer
B. Pafnuty L'vovich Chebyshev
Explanation
Pafnuty L'vovich Chebyshev, a Russian mathematician, attempted to prove the asymptotic law of distribution of prime numbers in two papers from 1848 and 1850.
6.
Pafnuty L'vovich Chebyshev is a mathematician from which country?
Correct Answer
A. Russia
Explanation
Pafnuty L'vovich Chebyshev is a mathematician from Russia.
7.
........ is concerned with the additive structure of the integers?
Correct Answer
A. Additive number theory
Explanation
Additive number theory is concerned with the additive structure of the integers. It focuses on the properties and relationships of addition in the context of number theory. This branch of mathematics explores topics such as partitions, arithmetic progressions, and additive bases. It aims to understand how integers can be combined together through addition and uncover patterns and properties related to this operation.
8.
......... deals with the distribution of the prime numbers?
Correct Answer
C. Multiplicative number theory
Explanation
Multiplicative number theory deals with the distribution of prime numbers. This branch of number theory focuses on studying the properties and patterns of prime numbers, including their distribution, relationships, and behavior under multiplication. It involves concepts such as the prime number theorem, prime factorization, and the study of multiplicative functions. By analyzing the multiplicative properties of numbers, this theory provides insights into the distribution of primes and their connections to other mathematical concepts.
9.
In what year did Bernhard Riemann used complex analysis and a special meromorphic function now known as the Riemann zeta function to derive an analytic expression for the number of primes less than or equal to a real number x.
Correct Answer
A. 1859
Explanation
In 1859, Bernhard Riemann used complex analysis and a special meromorphic function, now known as the Riemann zeta function, to derive an analytic expression for the number of primes less than or equal to a real number x.
10.
........ are concerned with integer solutions to polynomial equations?
Correct Answer
B. DiopHantine problem
Explanation
The Diophantine problem is concerned with finding integer solutions to polynomial equations. This problem is named after the ancient Greek mathematician Diophantus, who studied and wrote about these types of equations. The other options, additive number theory, multiplicative number theory, and divisive number theory, are not specifically focused on finding integer solutions to polynomial equations.