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- Riemann Riemann hypothesis Sum
In summary, the conversation discusses the Riemann hypothesis and its significance in mathematics. The speaker expresses fascination with the problem and wishes luck to those attempting to solve it. The conversation also mentions the moral implications of the hypothesis.
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Drakkith
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There's something about the Riemann hypothesis that fascinates me. And this is coming from a guy who had to take calc 2, calc 3, and diff eq twice each to pass them. It seems like such a simple problem, yet has profound implications in many different areas of math. Best of luck to all those trying to solve it!
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Drakkith said:
David Hilbert said:
"Mathematical Mysteries: The Beauty and Magic of Numbers". Book by Calvin C. Clawson, p. 258, 1999.
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ohwilleke
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Keep at it mathematicians!
It poses important moral dilemmas.
It poses important moral dilemmas.
FAQ: The Extended Riemann Hypothesis and Ramanujan’s Sum
What is the Extended Riemann Hypothesis?
The Extended Riemann Hypothesis is a conjecture in mathematics that extends the original Riemann Hypothesis, which is one of the most famous unsolved problems in mathematics. It states that all non-trivial zeros of the Riemann zeta function lie on the critical line with real part equal to 1/2.
Who proposed the Extended Riemann Hypothesis?
The Extended Riemann Hypothesis was proposed by the mathematician Bernhard Riemann in 1859. He was trying to find a pattern in the distribution of prime numbers and came up with the Riemann zeta function, which is the key to the hypothesis.
What is Ramanujan's Sum?
Ramanujan's Sum is a mathematical function named after the Indian mathematician Srinivasa Ramanujan. It is defined as the sum of all positive integers that can be expressed as the sum of two cubes in two different ways. For example, 1729 is a Ramanujan's Sum because it can be expressed as 1^3 + 12^3 and 9^3 + 10^3.
How is Ramanujan's Sum related to the Extended Riemann Hypothesis?
The Extended Riemann Hypothesis and Ramanujan's Sum are connected through the Riemann zeta function. Ramanujan's Sum can be expressed as a special case of the zeta function, and the Extended Riemann Hypothesis predicts the behavior of the zeta function, including the distribution of Ramanujan's Sum. Therefore, solving the Extended Riemann Hypothesis would also provide insights into Ramanujan's Sum.
Why is the Extended Riemann Hypothesis important?
The Extended Riemann Hypothesis has significant implications in number theory and has connections to other areas of mathematics, such as algebra, analysis, and geometry. It also has practical applications in cryptography and prime number generation. Its proof or disproof would have a major impact on our understanding of the distribution of prime numbers and the nature of the Riemann zeta function.