ELI5: Explain Like I'm 5

Siegel modular form

Have you ever played with LEGOs? You can use them to build all sorts of cool things, right? Well, imagine that instead of LEGOs, you have numbers. And instead of building things, you're making special shapes out of these numbers. These special shapes are called Siegel modular forms.

But what's so special about Siegel modular forms? Well, they can tell us a lot about a type of math called arithmetic geometry. This is all about studying the relationships between numbers and shapes.

Now, imagine that you have a bunch of numbers, like 1, 2, 3, and so on. But you can't just put them together however you want - there are some rules you have to follow. For example, if you add two even numbers together, you'll always get an even number. And if you multiply two odd numbers together, you'll always get another odd number.

Using these rules, you can create special shapes out of these numbers called Siegel modular forms. These shapes are really important in arithmetic geometry because they tell us things about the relationships between different types of numbers.

For example, some of these shapes might tell us about something called elliptic curves. These are special types of curves that show up a lot in arithmetic geometry. By studying the shapes of these Siegel modular forms, mathematicians can learn more about the properties of elliptic curves and how they behave.

So there you have it - Siegel modular forms are like special shapes made out of numbers that help mathematicians learn more about arithmetic geometry, especially when it comes to elliptic curves!