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\begin{document}
\begin{enumerate}
  \item Algebraic Number Theory
     \begin{enumerate}
       \item Invariants of number fields: rings of integers,
discriminants, orders
       \item Arithmetic of number fields: splitting of primes,
ramification, Frobenius, class groups
       \item Structure of units in number fields
       \item Binary quadratic forms
       \item Kronecker-Weber theorem
       \item Ideles, adeles
       \item Cebotarev density theorem, Artin reciprocity, class field theory
     \end{enumerate}

  \item Analytic Number Theory
     \begin{enumerate}
       \item Analytic properties of L-functions
       \item Primes in arithmetic progressions
       \item Siegel zero problem
       \item Prime number theorem and prime number theorem for
arithmetic progressions
       \item Large sieve inequality for multiplicative characters
     \end{enumerate}       
  \item Elliptic Curves
     \begin{enumerate}
       \item Elliptic curves over {\bf C}
       \item Elliptic curves over finite fields, Hasse's theorem
       \item Hasse-Weil L-functions
       \item Mordell-Weil theorem and descent on elliptic curves
       \item Complex multiplication
     \end{enumerate}
  \item Modular Forms
     \begin{enumerate}
       \item Modular forms for the full modular group and its
congruence subgroups
       \item Eisenstein series
       \item Mellin transforms, L-series, converse theorems
       \item Hecke operators
       \item Modular forms of half-integer weight
     \end{enumerate}
               
 


\end{enumerate}


\end{document}



	






