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Results tagged with nt.number-theory
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user 257465
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
0
votes
0
answers
209
views
Mertens function via Perron's formula without assuming the simplicity of the Riemann zeros
Let $\mu$ denote the Möbius function, and define the the Mertens function $M(x) = \sum_{n \leq x} \mu(n)$. By Person's formula, one can express $M(x)$ as a sum over the nontrivial zeros of the Rieman …
- 149
6
votes
1
answer
889
views
What is the best known upper bound for $\frac{1}{\zeta'(\rho)}$ assuming the SZC but not the...
Let $\zeta$ denote the Riemann zeta function and let $\rho$ denote one of its complex zeros. What is the best known upper bound for $\frac{1}{\zeta'(\rho)}$ assuming that all zeros are simple (SZC), b …
- 149
8
votes
2
answers
2k
views
Why is the Simple Zeros Conjecture said to be stronger than the Riemann Hypothesis?
Let the "Simple Zeros Conjecture (SZC)" be the statement that all zeros of the Riemann zeta function are simple.
I have often heard of the statement that the SZC is stronger than the Riemann Hypothesi …
- 149