Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Simonic, Aleksander"'
Conditional upper and lower bounds for $L$-functions in the Selberg class close to the critical line
Autor:
Palojärvi, Neea, Simonič, Aleksander
Assuming the Generalized Riemann Hypothesis, we provide uniform upper and lower bounds with explicit main terms for $\log{\left|\mathcal{L}(s)\right|}$ for $\sigma \in (1/2,1)$ and for functions in the Selberg class. We also provide estimates under a
Externí odkaz:
http://arxiv.org/abs/2410.22711
Autor:
Palojärvi, Neea, Simonič, Aleksander
Assuming the Generalized Riemann Hypothesis, we provide uniform upper bounds with explicit main terms for moduli of $\left(\cL'/\cL\right)(s)$ and $\log{\cL(s)}$ for $1/2+\delta\leq\sigma<1$, fixed $\delta\in(0,1/2)$ and for functions in the Selberg
Externí odkaz:
http://arxiv.org/abs/2211.01121
Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L'/L\right)\left(\sigma,\chi\right)$ of Dirichlet $L$-functions, where $\chi$ is a primitive character modulo $q\geq 10^
Externí odkaz:
http://arxiv.org/abs/2206.00819
Autor:
Simonič, Aleksander
Assuming the Generalized Riemann Hypothesis, we provide explicit upper bounds for moduli of $\log{\mathcal{L}(s)}$ and $\mathcal{L}'(s)/\mathcal{L}(s)$ in the neighbourhood of the 1-line when $\mathcal{L}(s)$ are the Riemann, Dirichlet and Dedekind z
Externí odkaz:
http://arxiv.org/abs/2201.10771
Autor:
Simonič, Aleksander
Assuming the Riemann Hypothesis, we provide effective upper and lower estimates for $\left|\zeta(s)\right|$ right to the critical line. As an application we make explicit Titchmarsh's conditional bound for the Mertens function and Montgomery--Vaughan
Externí odkaz:
http://arxiv.org/abs/2109.11744
Publikováno v:
J. Number Theory 244 (2023), 111-168
We provide an explicit $O\left(\log^2{T}\right)$-term of the celebrated Atkinson's formula for the error term $E(T)$ of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of wel
Externí odkaz:
http://arxiv.org/abs/2105.06821
Publikováno v:
In Indagationes Mathematicae January 2024 35(1):14-27
Autor:
Simonič, Aleksander
Assuming the Riemann Hypothesis, we provide explicit upper bounds for moduli of $S(t)$, $S_1(t)$, and $\zeta\left(1/2+\mathrm{i}t\right)$ while comparing them with recently proven unconditional ones. As a corollary we obtain a conditional explicit bo
Externí odkaz:
http://arxiv.org/abs/2010.13307
Autor:
Morrill, Thomas, Simonič, Aleksander
We establish quasimodularity for a family of residual crank generating functions defined on overpartitions. We also show that the second moments of these $k$th residual cranks admit a combinatoric interpretation as weighted overpartition counts.
Externí odkaz:
http://arxiv.org/abs/2005.01919
Autor:
Simonič, Aleksander
It is well-known that the straight gravity tunnel between any two different positions on a non-rotating Earth, which has uniform density, is traversable, i.e., an object initially at rest will reach its destination through the gravity tunnel in both
Externí odkaz:
http://arxiv.org/abs/2001.03279