Question

I really need help solving this !!

Answer 1

Image's formula estimates the count of "nontrivial zeros" of a famous math function, the Riemann zeta, lying on a specific line. These zeros hold mysteries about prime numbers.

The image you sent me shows a mathematical formula that is related to the Riemann zeta function, which is a function studied in number theory. The specific formula in the image is for the zeros of the Riemann zeta function. The Riemann zeta function is defined for complex numbers with a real part greater than 1 by the infinite series:

`$$\zeta(s) = \sum_(n=1)^(\infty) (1)/(n^(s))$$`

The zeta function has zeros at negative even integers and it is believed that it also has infinitely many non-real zeros. These non-real zeros are called the Riemann zeta function's nontrivial zeros. The location of the nontrivial zeros of the Riemann zeta function is a major unsolved problem in mathematics.

The formula in the image is related to the Riemann zeta function's zeros because it gives an estimate for the number of zeros of the Riemann zeta function that lie on a certain line in the complex plane. The line in question is the line with real part
`$\sigma$` and imaginary part t, where $\sigma$ and t are real numbers. The formula in the image gives an estimate for the number of zeros of the Riemann zeta function that lie on this line for values of t between 0 and T.

The formula in the image is given by:

`$$N(\sigma,T) = (T)/(2\pi) \log T + (1)/(2) \log ((1-\sigma)/2) + O(log T)$$`

where
`$O(log T)$` is a quantity that is bounded by a constant multiple of
`$\log T$`.

The formula in the image is important because it provides a way to estimate the number of zeros of the Riemann zeta function on a certain line in the complex plane. This can help mathematicians to better understand the distribution of the Riemann zeta function's zeros.