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Number Theory

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Statements about the Riemann Zeta Function

NUMTH-IYBSLM

Which of the following is true about the Riemann zeta function?

A

The Riemann zeta function, denoted by $\zeta :\{ s \in \mathbb{C} ~|~ \text{Re}(s) > 1\} \rightarrow \mathbb{C}$, satisfies the identity: $$\zeta(s) = \sum_{n = 1}^{\infty} \frac{1}{n^s}$$

B

The Riemann zeta function, denoted by $\zeta : \mathbb{C} \rightarrow \mathbb{C}$, satisfies the identity: $$\zeta(s) = \sum_{n = 1}^{\infty} \frac{1}{n^s}$$

C

The Riemann zeta function, denoted by $\zeta :\{ s \in \mathbb{C} ~|~ \text{Re}(s) \leq 1\} \rightarrow \mathbb{C}$, satisfies the identity: $$\zeta(s) = \sum_{n = 1}^{\infty} \frac{1}{n^s}$$

D

The Riemann zeta function satisfies the identity: $$\zeta(s) = \sum_{n = 1}^{\infty} \frac{1}{n^s}$$