Journal of Undergraduate Research
Keywords
modular forms, modulo powers, primes, elliptic curves
College
Physical and Mathematical Sciences
Department
Mathematics
Abstract
Modular forms are constructs of complex analysis that possess many intricate connections to widely-separated branches of mathematics. In the most well-known application of these functions, Andrew Wiles established a connection between the Fourier coefficients of modular forms and elliptic curves–objects of analytic geometry–in order to prove Fermat’s Last Theorem, a classical number theory problem that had resisted proof for more than 350 years. Modular forms have also found applications ranging from cryptography to the million-dollar Birch and Swinerton-Dyer conjecture.
Recommended Citation
Griffin, Michael and Jenkins, Dr. Paul
(2014)
"Up Congruences of Modular Functions Modulo Powers of Primes,"
Journal of Undergraduate Research: Vol. 2014:
Iss.
1, Article 1210.
Available at:
https://scholarsarchive.byu.edu/jur/vol2014/iss1/1210