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/sci/ - Science & Math

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5143806 No.5143806 [Reply] [Original]

I want to study number theory, but I don't know what to focus on to be able to really have a good foundation in it. Should I focus on algebraic or analytic number theory? Or are both considered necessities for anyone wanting to do number theoretic research?

In particular, I'm interested in the distribution of prime numbers, so things like the Riemann zeta function, arithmetic progressions, etc.

>> No.5144115

>>5143806
>pic
cool dragon curve construction, bro!

>> No.5144153

>>5144115
it's really cool, i wish it would go more iterations.

>> No.5144515

bump

>> No.5144539

Analytic is more about integers (and particularly Riemann), but there is always cross-pollination. Certainly couldn't hurt to do both... you won't know for sure what you'll like until you try. Some combinatorics would also be useful, and some algebra. Elliptic curves have (probably) solved two huge number theoretic problems in the last few decades, and very few people understand them well, so that's a good place to go.

>> No.5144638

>>5144539
Where exactly do elliptic curves fall? Is it algebraic number theory? Algebraic geometry?

>> No.5144858

>>5144638
all of the above
elliptic curves and modular forms combine the analytic and the algebraic (along with geometry)