AbstractLet[formula]where the inner-most sum runs over the imaginary partsγof zeros of DirichletL-functionsL(s,χ) and where[formula]andK(s) is a suitably chosen “kernel.” Under the assumption of the Generalized Riemann Hypothesis we estimate the asymptotic size ofFK(α,Q) asQ→+∞ in the range ∣α∣<2. This is used to prove that the proportion of simple zeros of all DirichletL-functions is greater than or equal to1112in the sense of the inequality[formula]asQ→+∞
AbstractSelberg has shown on the basis of the Riemann hypothesis that for every ε > 0 most intervals...
This thesis consists of three projects. The first project focuses on the distribution of zeros of l...
In early 1970s, Hugh Montgomery initialized the study of the pair correlation function F(X,T) on zer...
We investigate the pair correlation function of the zeros of Dirichlet L-functions, namely F((alpha)...
Montgomery’s pair correlation conjecture predicts the asymptotic behavior of the function N(T, β) de...
We define a function which correlates the zeros of two Dirichlet L-functions to the modulus q and we...
We define a function which correlates the zeros of two Dirichlet L-functions to the modulus q and we...
We establish, via a heuristic Fourier inversion calculation, that the Hardy–Littlewood twin prime co...
AbstractOur main discovery is the inequalityD(A, BD[A, B]⩾DADB,whereA,Bare arbitrary sets of positiv...
Ahlswede R, Khachatrian LH. Number theoretic correlation inequalities for Dirichlet densities. JOURN...
Assume the Riemann Hypothesis and let $F(X,T)=4\sum\limits_{0<\gamma_1,\gamma_2\leq T}\frac{X^{i...
This is the author accepted manuscript. The final version is available from Springer Verlag via the ...
Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e...
summary:We study tails of prime counting functions. Our approach leads to representations with a mai...
Nonlinearity has published articles containing a significant number-theoretic component since the jo...
AbstractSelberg has shown on the basis of the Riemann hypothesis that for every ε > 0 most intervals...
This thesis consists of three projects. The first project focuses on the distribution of zeros of l...
In early 1970s, Hugh Montgomery initialized the study of the pair correlation function F(X,T) on zer...
We investigate the pair correlation function of the zeros of Dirichlet L-functions, namely F((alpha)...
Montgomery’s pair correlation conjecture predicts the asymptotic behavior of the function N(T, β) de...
We define a function which correlates the zeros of two Dirichlet L-functions to the modulus q and we...
We define a function which correlates the zeros of two Dirichlet L-functions to the modulus q and we...
We establish, via a heuristic Fourier inversion calculation, that the Hardy–Littlewood twin prime co...
AbstractOur main discovery is the inequalityD(A, BD[A, B]⩾DADB,whereA,Bare arbitrary sets of positiv...
Ahlswede R, Khachatrian LH. Number theoretic correlation inequalities for Dirichlet densities. JOURN...
Assume the Riemann Hypothesis and let $F(X,T)=4\sum\limits_{0<\gamma_1,\gamma_2\leq T}\frac{X^{i...
This is the author accepted manuscript. The final version is available from Springer Verlag via the ...
Assume the Riemann Hypothesis and a weaker form of Montgomery's pair correlation conjecture, i.e...
summary:We study tails of prime counting functions. Our approach leads to representations with a mai...
Nonlinearity has published articles containing a significant number-theoretic component since the jo...
AbstractSelberg has shown on the basis of the Riemann hypothesis that for every ε > 0 most intervals...
This thesis consists of three projects. The first project focuses on the distribution of zeros of l...
In early 1970s, Hugh Montgomery initialized the study of the pair correlation function F(X,T) on zer...
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