We’re here to learn together.

To set the stage: L-functions. These bad boys are a type of mathematical function used in number theory (which is basically math for nerds). They have some pretty cool properties, like being able to tell us if certain numbers are prime or not. But that’s not what we’re here to talk about today.

Instead, let’s focus on the connection between L-functions and elliptic curves. Elliptic curves are a type of mathematical object used in cryptography (which is basically math for spies). They have some pretty cool properties too, like being able to keep secrets really well. But that’s not what we’re here to talk about today either.

So why do L-functions and elliptic curves go together? Well, it turns out that there’s a relationship between the zeros of certain L-functions and the points on certain elliptic curves. This is known as the “L-function/Elliptic Curve Conjecture,” which is basically math speak for “we think these two things are related.”

Now, you might be wondering why we care about this relationship between L-functions and elliptic curves. Well, it turns out that understanding this connection could have some pretty big implications in the world of cryptography. For example, if we can find a way to use L-functions to analyze the security of certain elliptic curve cryptosystems, then we might be able to make them even more secure than they already are!

But that’s not all. The relationship between L-functions and elliptic curves has also led to some pretty cool math problems. For example, there’s a famous problem known as the “Birch and Swinnerton-Dyer Conjecture,” which is basically asking if we can use L-functions to count the number of points on certain elliptic curves. This might sound like a simple question, but it turns out that it’s actually really hard to answer!

Two seemingly unrelated topics in math that are actually pretty closely related. Who knew?