Modular forms - NMAG462
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Modular forms are central objects in modern number theory, which played an important role in the proof of
Fermat's Last Theorem. They are certain complex functions encoding information of number-theoretic interest,
e.g., about the numbers of solutions of diophantine equations. Combining analytic and algebraic methods, the
course will cover their basic properties and some applications. The course may not be taught every academic
year, it is taught at least once per two years.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (03.06.2025)
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J. S. Milne: Modular Functions and Modular Forms, S. Lang: Algebraic Number Theory, Second Edition, GTM, Springer 1994 F. Diamond, J. Shurman: A First Course in Modular Forms, GTM, Springer 2005 D. Bump: Automorphic Forms and Representations, Cambridge Studies in Advanced Mathematics 55 (1998) Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (10.05.2017)
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Students have to pass final oral exam. The requirements for the exam correspond to what has been done during lectures. Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (28.10.2019)
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Riemann surfaces Upper half plane and SL(2, R) Elliptic functions Modular forms Eisenstein's series, Ramanujan's tau function Hecke operators Zeta function and Dirichlet L-functions Analytic continuation and functional equation Theta functions L-functions of modular forms and elliptic curves FLT and modularity theorem Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (10.05.2017)
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