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Full-Text Articles in Physical Sciences and Mathematics
Level Stripping Of Genus 2 Siegel Modular Forms, Rodney Keaton
Level Stripping Of Genus 2 Siegel Modular Forms, Rodney Keaton
All Dissertations
In this Dissertation we consider stripping primes from the level of genus 2 cuspidal Siegel eigenforms. Specifically, given an eigenform of level Nlr which satisfies certain mild conditions, where l is a prime not dividing N, we construct an eigenform of level N which is congruent to our original form. To obtain our results, we use explicit constructions of Eisenstein series and theta functions to adapt ideas from a level stripping result on elliptic modular forms. Furthermore, we give applications of this result to Galois representations and provide evidence for an analog of Serre's conjecture in the genus 2 case.
Solving Diophantine Equations, Florentin Smarandache, Octavian Cira
Solving Diophantine Equations, Florentin Smarandache, Octavian Cira
Branch Mathematics and Statistics Faculty and Staff Publications
In recent times, we witnessed an explosion of Number Theory problems that are solved using mathematical software and powerful computers. The observation that the number of transistors packed on integrated circuits doubles every two years made by Gordon E. Moore in 1965 is still accurate to this day. With ever increasing computing power more and more mathematical problems can be tacked using brute force. At the same time the advances in mathematical software made tools like Maple, Mathematica, Matlab or Mathcad widely available and easy to use for the vast majority of the mathematical research community. This tools don’t only …