Asymptotic minimax testing of independence hypothesis

1989 ◽  
Vol 44 (4) ◽  
pp. 466-476 ◽  
Author(s):  
Yu. I. Ingster
Keyword(s):  
Minimax Testing ◽  
Asymptotic Minimax ◽  
Independence Hypothesis

scholarly journals Limiting Properties of the Distribution of Primes in an Arbitrarily Large Number of Residue Classes

2020 ◽  
Vol 63 (4) ◽  
pp. 837-849 ◽  
Author(s):  
Lucile Devin
Keyword(s):  
Riemann Hypothesis ◽  
Linear Independence ◽  
Classical Case ◽  
Weak Version ◽  
Distribution Of Primes ◽  
Logarithmic Density ◽  
Fixed Integer ◽  
Residue Classes ◽  
Independence Hypothesis ◽  
And Function

AbstractWe generalize current known distribution results on Shanks–Rényi prime number races to the case where arbitrarily many residue classes are involved. Our method handles both the classical case that goes back to Chebyshev and function field analogues developed in the recent years. More precisely, let $\unicode[STIX]{x1D70B}(x;q,a)$ be the number of primes up to $x$ that are congruent to $a$ modulo $q$. For a fixed integer $q$ and distinct invertible congruence classes $a_{0},a_{1},\ldots ,a_{D}$, assuming the generalized Riemann Hypothesis and a weak version of the linear independence hypothesis, we show that the set of real $x$ for which the inequalities $\unicode[STIX]{x1D70B}(x;q,a_{0})>\unicode[STIX]{x1D70B}(x;q,a_{1})>\cdots >\unicode[STIX]{x1D70B}(x;q,a_{D})$ are simultaneously satisfied admits a logarithmic density.

Isospin and the Bohr Independence Hypothesis

1972 ◽  
Vol 5 (2) ◽  
pp. 463-476 ◽  
Author(s):  
Louis C. Vaz ◽  
C. C. Lu ◽  
J. R. Huizenga
Keyword(s):  
Independence Hypothesis
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