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Full-Text Articles in Physical Sciences and Mathematics
Obstruction Criteria For Modular Deformation Problems, Jeffrey Hatley Jr
Obstruction Criteria For Modular Deformation Problems, Jeffrey Hatley Jr
Doctoral Dissertations
For a cuspidal newform f of weight k at least 3 and a prime p of the associated number field Kf, the deformation problem for its associated mod p Galois representation is unobstructed for all primes outside some finite set. Previous results gave an explicit bound on this finite set for f of squarefree level; we modify this bound and remove the squarefree hypothesis. We also show that if the p-adic deformation problem for f is unobstructed, then f is not congruent mod p to a newform of lower level.
The Fourier Coefficients Of Modular Forms, Kyle Pratt, Dr. Paul Jenkins
The Fourier Coefficients Of Modular Forms, Kyle Pratt, Dr. Paul Jenkins
Journal of Undergraduate Research
Modular forms are complex analytic functions with remarkable properties. Modular forms possess interesting and surprising connections to many different branches of mathematics. For example, it is well-known that Andrew Wiles’ proof of Fermat’s Last Theorem, a conjecture that had been unresolved for more than three centuries, utilized modular forms in a crucial way.