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In this article, we study the distribution of large values of the Riemann zeta function on the 1-line. We obtain an improved distribution function concerning large values, holding in the same range as that given by Granville and Soundararajan.

We investigate the large values of the derivatives of the Riemann zeta function$\\zeta (s)$on the 1-line. We give a larger lower bound for$\\max _{t\\in [T,2T]}|\\zeta ^{(\\ell )}(1+{i} t)|$, which improves the previous result established by Yang [‘Extreme values of derivatives of the Riemann zeta function’, Mathematika 68 (2022), 486–510].

We investigate the large values of the derivatives of the Riemann zeta function $\\zeta (s)$ on the 1-line. We give a larger lower bound for $\\max _{t\\in [T,2T]}|\\zeta ^{(\\ell )}(1+{i} t)|$ , which improves the previous result established by Yang [‘Extreme values of derivatives of the Riemann zeta function’, Mathematika 68 (2022), 486–510].

Let ℓ be a fixed natural number. We study the conditional upper bounds and extreme values of derivatives of the Riemann zeta function | ζ ( ℓ ) ( σ + i t ) | and Dirichlet L -functions L ( ℓ ) ( σ , χ ) with χ ( mod q ) , where σ is close to 1. We show that, if | σ - 1 | ≪ 1 / log 2 t , then | ζ ( ℓ ) ( σ + i t ) | has the same maximal order (up to the leading coefficients) as | ζ ( ℓ ) ( 1 + i t ) | when t → ∞ . Similar results can be obtained for Dirichlet L -functions L ( ℓ ) ( σ , χ ) with χ ( mod q ) nonprincipal.

In this article, we apply the resonance method to derive conditional Omega results for logarithmic derivatives of quadratic Dirichlet \\(L\\)-functions. We improve a previous result of Mortada and Murty \\cite{MM13}, as well as generalize some results of Yang \\cite{yang2023omegatheoremslogarithmicderivatives}.

There are many results for explicit expressions about \\(q\\)-multiple zeta values or \\(q\\)-harmonic sums on \\(A-\\cdots-A\\) indices, that is, the indices are the same. Though the way to treat \\(q\\)-multiple zeta values unless the indices are the same, it has been successful to get the explicit expression of \\(q\\)-harmonic sums on \\(1-\\cdots-1,2,1-\\cdots-1\\) indices. In this paper, we shall consider more general results when the ratio of indices of \\(2\\) to indices of \\(1\\) increases.

In this article, we investigate conditional large values of quadratic Dirichlet character sums. We prove some Omega results of quadratic character sums under the assumption of the generalized Riemnn hypothesis, which are as sharp as previous results for all characters modulo a large prime.

We investigate the distribution of large values of the Riemann zeta function \\(\\zeta(s)\\) in the strip \\(1/2<\\re s<1\\). For any fixed \\(\\re s=\\sigma\\in(1/2,1)\\), we obtain an improved distribution function of large values of \\(|\\zeta(\\sigma+\\i t)|\\), holding in the same range as that given by Lamzouri.

In this article, we study the distribution of large values of the Riemann zeta function on the 1-line. We obtain an improved density function concerning large values, holding in the same range as that given by Granville and Soundararajan.

We investigate the large values of the derivatives of the Riemann zeta function \\(\\zeta(s)\\) on the 1-line. We give a larger lower bound for \\(\\max_{t\\in[T,2T]}|\\zeta^{(\\ell)}(1+{\\rm i} t)|\\), which improves the previous result established by Yang.