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MATH 68005 Special Topics in MATH: Analytic Number Theory Select Term:
1 - Ability to utilize the properties of arithmetic functions, compute their average orders. 2 - Ability to apply elementary theorems on distribution of primes, knowledge of the prime number theorem. 3 - Thorough understanding of Dirichlet's theorem on primes in arithmetic progressions. 4 - Basic ability to manipulate Dirichlet series, Euler products, zeta-and L-functions. 5 - Basic understanding of the components of the proof of the prime number theorem. * Arithmetic functions. * Big-oh notation and average orders of arithmetic functions. * Elementary theorems on the distribution of prime numbers, introduction to the prime number theorem. * Characters of finite abelian groups. * Dirichlet's theorem on primes in arithmetic progressions. * Dirichlet series and Euler products. * Zeta- and L-functions. * Analytic proof of the prime number theorem.
SU Credits : 3
ECTS Credit : 10
Prerequisite : -
Corequisite : -