Notes on Speyer’s paper titled “Some Sums over Irreducible Polynomials”

Let be the set of irreducible polynomials over . Then . The paper lists certain examples of below. These are all expanded as geometric series. As one can see only contribute to the coefficient of in the sum . Why don’t the other irreducible polynomials do the same? This is because these are the onlyContinue reading “Notes on Speyer’s paper titled “Some Sums over Irreducible Polynomials””

Puiseux Series and Tropical Varieties

Puiseux series- This field is denoted by . Note that we have a double brace “[[ ]]” instead of “[]”. This implies that we have infinite series instead of finite ones (which would be polynomials). The Puiseux laurent series is denoted as . This means that is also allowed to have negative powers. Now ,Continue reading “Puiseux Series and Tropical Varieties”