Modular forms and L-functions II - NMAG473
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Modular forms and L-functions 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 distribution of prime numbers, or numbers of
solutions of diophantine equations. Combining analytic and algebraic
methods, the course will cover their basic properties and some
applications. Specific choice of topics will depend on the interests of
participants.
The course may not be taught every academic year.
Last update: Žemlička Jan, doc. Mgr. et Mgr., Ph.D. (14.05.2019)
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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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Zkouška bude ústní s 30-60 minutami na přípravu jedné nebo dvou otázek, odpovídajících probrané látce na přednáškách. Last update: Kala Vítězslav, doc. Mgr., Ph.D. (14.02.2018)
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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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