| Title | Date | Views | Brief Description |
|---|
| Algorithms for enumerating invariants and extensions of local fields |
2015 |
1332 |
There are many computationally difficult problems in the study of p-adic fields, among them the classification of field extensions and the decomposition of global ideals. The main goal of this work is present efficient algorithms, leveraging the Newt... |
| Computing Galois groups of Eisenstein polynomials over p-adic fields |
2017 |
2501 |
The most efficient algorithms for computing Galois groups of polynomials over global fields are based on Stauduhar’s relative resolvent method. These methods are not directly generalizable to the local field case, since they require a field that cont... |
| Symbolic computation of resolvents |
2017 |
1320 |
Resolvent polynomials are used in the determination of Galois groups of polynomials. The computation of the resolvent usually relies on root approximations requiring a high degree of precision. Leonard Soicher developed a method to compute absolute l... |
| Results about fractional derivatives of Zeta functions |
2017 |
1148 |
Perhaps the most important function in all mathematics is the Riemann Zeta function. For almost 150 years Mathematicians have tried to understand the behavior of the function’s complex zeros. Our main aim is to investigate properties of the Riemann Z... |
| On generators of Hilbert modular groups of totally real number fields |
2016 |
1667 |
In this paper we report the beginnings of the computations and tabulations of the generators of $\PSL_2(\OK)$, where $\OK$ is the maximal order of a real field of degree $n=[K:\QQ]$. We discuss methods of obtaining generators in order to calculate th... |
| On zeros of fractional derivatives of Dirichlet series and polynomials |
2024 |
127 |
In this thesis we apply some of the important concepts of Complex Analysis and Fractional Calculus to several special functions from Analytic Number Theory. For Euler eta, Dirichlet L-functions and polynomials we establish new zero-free regions and e... |