Expedition 2: Real vs Imaginary Crossings

Overview

[Content placeholder: How Re(ζ(s)) and Im(ζ(s)) cross zero independently. Three types of crossings: real-only, imaginary-only, and simultaneous (true zeros).]

The Mathematical Background

[Placeholder: Explain real and imaginary components, what it means for each to cross zero separately]

What This Expedition Studies

[Placeholder: Crossing frequencies, statistical distribution of Type A (real-only), Type B (imaginary-only), and Type C (complete) crossings]

Visualizations

What We've Observed

• Placeholder: Initial observations about crossing frequencies
• Hypothesis: Type A and Type B appear equally frequent

What We're Curious About Next

• Does the functional equation predict crossing statistics?
• Is the ratio constant or does it vary with height?