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A typical book can be printed with 10 6 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 94 such books to print all the zeros of a googolplex (that is, printing a googol zeros). [4] If each book had a mass of 100 grams, all of them would have a total mass of 10 93 kilograms.
A googol is the large number 10 100 or ten to the power of one hundred. In decimal notation, it is written as the digit 1 followed by one hundred zeros: 10, 000, 000 ...
The Riemann zeta function ζ(z) plotted with domain coloring. [1] The pole at = and two zeros on the critical line.. The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (), is a mathematical function of a complex variable defined as () = = = + + + for >, and its analytic continuation elsewhere.
This is a description of what would happen if one tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex is, then, a specific finite number, equal to 1 with a googol zeros after it.
In 1992 Karatsuba proved [5] that an analog of the Selberg conjecture holds for "almost all" intervals (T, T + H], H = T ε, where ε is an arbitrarily small fixed positive number. The Karatsuba method permits one to investigate zeroes of the Riemann zeta function on "supershort" intervals of the critical line, that is, on the intervals (T, T ...
Zeros of the Riemann zeta except negative even integers are called "nontrivial zeros". The Riemann hypothesis states that the real part of every nontrivial zero must be 1 / 2 . In other words, all known nontrivial zeros of the Riemann zeta are of the form z = 1 / 2 + yi where y is a real number.
This implies that all zeros of P k (T) lie on the "critical line" of complex numbers s with real part k/2. 4. (Betti numbers) If X is a (good) "reduction mod p" of a non-singular projective variety Y defined over a number field embedded in the field of complex numbers, then the degree of P i is the i th Betti number of the space of complex ...
Because of the order of zeros and poles being defined as a non-negative number n and the symmetry between them, it is often useful to consider a pole of order n as a zero of order –n and a zero of order n as a pole of order –n. In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0.