Riemann Hypothesis and its Applications

Overview Riemann Hypothesis is one of the most important unresolved conjectures in mathematics. It connects the distribution of prime numbers with zeroes of Zeta function, defined on the complex plane. A number of algorithms in algebra and number theory rely on the correctness of Riemann Hypothesis or its generalizations - This course will describe the connection between prime distributions and Zeta function leading to the Riemann Hypothesis proving Prime Number Theorem along the way. It will then investigate generalizations of Riemann Hypothesis and their applications to computer science problem

Beginner 0(0 Ratings) 0 Students enrolled English
Created by skill expert
Last updated Fri, 17-Jun-2022
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Course overview

Prime counting and other arithmetic functions - Brief overview of complex analysis - Zeta function definition and basic properties - Riemann Hypothesis and its relationship with prime counting - Prime Number Theorem - Dirichlet L-functions and Extended Riemann Hypothesis - Applications of Riemann and Extended Riemann Hypothesis - Generalized Riemann Hypothesis, and its proof for functions fields, finite fields, and elliptic curves

Curriculum for this course
27 Lessons 22:09:35 Hours
Lecture
27 Lessons 22:09:35 Hours
  • Lecture 1
    Preview 00:41:43
  • Lecture 2
    00:45:23
  • Lecture 3
    00:46:19
  • Lecture 4
    00:46:30
  • Lecture 5
    00:59:08
  • Lecture 6
    00:51:15
  • Lecture 7
    00:50:55
  • Lecture 8
    00:57:50
  • Lecture 9
    00:43:25
  • Lecture 10
    00:55:08
  • Lecture 11
    00:51:12
  • Lecture 12
    00:38:15
  • Lecture 13
    00:51:52
  • Lecture 14
    00:57:41
  • Lecture 15
    00:50:33
  • Lecture 16
    00:55:28
  • Lecture 17
    00:43:45
  • Lecture 18
    01:20:56
  • Lecture 19
    00:42:59
  • Lecture 20
    00:38:33
  • Lecture 21
    00:37:53
  • Lecture 22
    00:42:36
  • Lecture 23
    00:34:00
  • Lecture 24
    01:28:53
  • Lecture 25
    00:54:19
  • Lecture 26
    00:27:31
  • Lecture 27
    00:35:33
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