Primes are to Irreducible Polynomials as Prime-related theorems are to ?? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-20T08:52:52Z http://mathoverflow.net/feeds/question/77968 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77968/primes-are-to-irreducible-polynomials-as-prime-related-theorems-are-to Primes are to Irreducible Polynomials as Prime-related theorems are to ?? SigmaX 2011-10-12T22:28:37Z 2011-10-13T05:41:39Z <p>Irreducible polynomials are often introduced as the analog to prime numbers in polynomial rings. Prime numbers, of course, have a very rich theory, leading to the likes of the Riemann Zeta function and the Prime Number Theorem.</p> <p>Do any analogs and/or generalizations of primes, such as irreducible polynomials and prime elements, have similarly rich theorems/conjectures?</p> http://mathoverflow.net/questions/77968/primes-are-to-irreducible-polynomials-as-prime-related-theorems-are-to/77999#77999 Answer by Gerry Myerson for Primes are to Irreducible Polynomials as Prime-related theorems are to ?? Gerry Myerson 2011-10-13T05:41:39Z 2011-10-13T05:41:39Z <p>Maybe the first generalization of prime numbers is to prime ideals in algebraic number fields. You do get analogs of the zeta-function, the Prime Number Theorem, even the Riemann Hypothesis. Any text on algebraic number theory will take you there. </p>