Visualizing the Riemann zeta function and analytic continuation

The video explores the Riemann Hypothesis, a significant unsolved problem in mathematics, and its connection to the Riemann Zeta function. It explains the concept of analytic continuation and how it extends the Zeta function beyond its original domain. The video also discusses the importance of the Zeta function's zeros, particularly in relation to prime numbers, and introduces complex exponents and their visualization. The Riemann Hypothesis posits that all non-trivial zeros of the Zeta function lie on a critical line, a conjecture with profound implications for number theory.

How does the Zeta function extend into the left half of the complex plane?

What are trivial zeros and how do they relate to the Zeta function?

Discuss the implications of proving the Riemann Hypothesis.

What is the significance of the sum 1 + 2 + 3 + 4 + ... in relation to the Zeta function?