No Zeros on the line Re(s)=1
In the study of analytic number theory, the behavior of the Riemann zeta function, is of central importance. Understanding the zeros of ζ(s), particularly where they lie in the complex plane, is a key area of research in mathematics.
One of the most significant results in this context is Hadamard’s 1896 proof that the Riemann zeta function has no zeros with real part equal to 1.
Hadamard’s approach to this problem is a remarkable application of advanced techniques in complex analysis.
In this lesson, we will explain Hadamard’s proof in detail, examining the tools and strategies he employed.
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