me22b003.tex

\section{ME22B003}
        The topic of my interest is \textbf{Riemann zeta function},which is useful in number theory for investigating properties of prime numbers. Written as $\zeta>
\begin{equation*}
                \text{$\zeta(x)$} = \sum_{n=1}^{\infty} \frac{1}{n^x} = \
        1 + \frac{1}{2^x} + \frac{1}{3^x} + \frac{1}{4^x} + \cdots\\
\end{equation*}

        \textit{\begin{center}
                \textbf{where x can be any real number}
        \end{center}}
        When x = 1, this series is called the \textit{harmonic series}, which increases without bound—i.e., \textbf{its sum is infinite}. For values of x larger tha>

        \footnote{\url{Britannica, The Editors of Encyclopaedia. "Riemann zeta function". Encyclopedia Britannica, 30 Dec. 2022, https://www.britannica.com/science/>
        The theory of the Riemann zeta-function and its generalisations represent one of the most beautiful developments in mathematics. The Riemann zeta-function i>
        \footnote{\textbf{Patterson, Samuel J. An introduction to the theory of the Riemann zeta-function. No. 14. Cambridge University Press,\textit{Preface},1995.}
        }\\
        \section{Summary}
        This Riemann zeta function are now used in the most intensely studied in number theory\\
        \textbf{\textit{Professor patterson}} has emphasized central ideas of broad application,avoiding technical results and the customary function theoretic appr>
        \\
        \emph{Name: \textbf{Balasoorya S}} \\
        \emph{GithubID: \textbf{BalasooryaSuresh}} \\