Fatma Çi̇çek
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View article: A Central Limit Theorem for Linear Combinations of Logarithms of Dirichlet $L$-functions Sampled at the Zeros of the Zeta Function
A Central Limit Theorem for Linear Combinations of Logarithms of Dirichlet $L$-functions Sampled at the Zeros of the Zeta Function Open
Let $L(s, χ_1), \ldots, L(s, χ_N)$ be primitive Dirichlet $L$-functions different from the Riemann zeta function. Under suitable hypotheses we prove that any linear combination $a_1\log|L(ρ,χ_1)|+\dots+a_N\log|L(ρ,χ_N)|$ has an approximate…
View article: The uniform distribution modulo one of certain subsequences of ordinates of zeros of the zeta function
The uniform distribution modulo one of certain subsequences of ordinates of zeros of the zeta function Open
On the assumption of the Riemann hypothesis and a spacing hypothesis for the nontrivial zeros $1/2+i\gamma$ of the Riemann zeta function, we show that the sequence \begin{equation*}\Gamma_{[a, b]} =\Bigg\{ \gamma : \gamma>0 \quad \mbox{and…
View article: Mean values of long Dirichlet polynomials with divisor coefficients
Mean values of long Dirichlet polynomials with divisor coefficients Open
In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower order terms and a power saving error term. This is deri…
View article: A Central Limit Theorem for Linear Combinations of Logarithms of Dirichlet $L$-functions
A Central Limit Theorem for Linear Combinations of Logarithms of Dirichlet $L$-functions Open
The purpose of this paper is to generalize our earlier work on the logarithm of the Riemann zeta-function to linear combinations of logarithms of primitive Dirichlet $L$-functions with constant real coefficients. Under the assumption of su…
View article: On the logarithm of the Riemann zeta-function near the nontrivial zeros
On the logarithm of the Riemann zeta-function near the nontrivial zeros Open
Assuming the Riemann hypothesis and Montgomery's Pair Correlation Conjecture, we investigate the distribution of the sequences $(\log|ζ(ρ+z)|)$ and $(\argζ(ρ+z)).$ Here $ρ=\frac12+iγ$ runs over the nontrivial zeros of the zeta-function, $0