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Qiyu Yang

Publications and source records attributed to Qiyu Yang.

11 recordsLinked to original sources
arXiv2026

Extreme values of derivatives of Dedekind zeta functions on the $1$-line

In this paper, we establish lower bounds for extreme values of derivatives of Dedekind zeta functions on the \(1\)-line over arbitrary fixed number fields. Our result extends Yang's corresponding estimate for the Riemann zeta function in 2024, with the leading constant involving residues of Dedekind zeta functions and a moment of the Dickman function. A key ingredient is a uniform asymptotic formula for weighted friable sums involving the coefficients of Dedekind zeta functions.

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arXiv2026

Extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus

In this paper, we obtain extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus. Our result yields a larger lower bound for extreme values than that from Soundararajan's classical resonance method. Consequently, we show that one branch of the dichotomy established by Bondarenko, Darbar, Hagen, Heap, and Seip (2023) can be realized for this family of Dirichlet $L$-functions. The proof relies on the resonance method together with precise estimates for GCD sums.

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arXiv2026

Large values of the Hurwitz zeta function with rational parameter

In this paper, we establish lower bounds for large values of the Hurwitz zeta function with rational parameter when the real part $σ\in [1/2,1]$. These results improve the earlier results of Ramachandra and Sankaranarayanan in 1989. On the critical line, our result recovers the corresponding lower bound of de la Bretèche and Tenenbaum (2019) for the Riemann zeta function, while for $1/2< σ\leq 1$, our lower bounds attain the same order as the corresponding lower bounds for large values of the Riemann zeta function. Our proofs are based on the resonance method.

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arXiv2026

An Omega result for partial sums of the Riemann zeta function

In this paper, we establish an Omega result for partial sums of the Riemann zeta function on the \(1\)-line. Our work relies on the long resonance method and an effective asymptotic formula for smooth numbers. For sufficiently long partial sums, our result approaches the work obtained by Aistleitner, Mahatab and Munsch in 2019.

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arXiv2026

Extreme values of the real part of the Riemann zeta function

In this paper, we establish lower bounds for extreme values of the real part of the Riemann zeta function on the critical line. This work relies on the resonance method of Bondarenko and Seip, together with lower bounds for certain integrals associated with Dirichlet series with non-negative coefficients. Our results extend the work of Bondarenko and Seip (2018).

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arXiv2026

Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field

In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convolution formula and combing special GCD sums, our result generalizes the work of Bondarenko et al. in 2023. We also set a lower bound by the resonance method when the real part is near the critical line, both of the above results refine part of Yang's work in 2022.

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arXiv2026

Joint extreme values of the Riemann zeta function at harmonic points

Using the resonance method, we obtain refined estimates for joint extreme values of the Riemann zeta function at harmonic points, improving upon Levinson's 1972 results and providing new insight into the behavior of the Riemann zeta function. Our proof is primarily based on Dirichlet series theory and the truncated Euler product for the Riemann zeta function. As a corollary, we can recover some previously known extreme value results for the zeta function.

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arXiv2025

An improved upper bound for the distribution of iterated Euler totient functions

Let $ϕ(n)$ be the Euler totient function and $ϕ_k(n)$ its $k$-fold iterate. In this note, we improve the upper bound for the number of positive $n\leqslant x$ such that $ϕ_{k+1}(n)\geqslant cn$. Comparing with the upper bound which was obtained from Pollack's asymptotic formula of the summation of $ϕ_{k+1}(n)$ for $n\leqslant x$, we have successfully increased the denominator exponent of the main term of the upper bound from $k$ to $k+1$.

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arXiv2025

On the Composition of the Euler Function and the Dedekind Arithmetic Function

Let $I(n) = \frac{ψ(ϕ(n))}{ϕ(ψ(n))}$ and $K(n) = \frac{ψ(ϕ(n))}{ϕ(ϕ(n))}$, where $ϕ(n)$ is Euler's function and $ψ(n)$ is Dedekind's arithmetic function. We obtain the maximal order of $I(n)$, as well as the average orders of $I(n)$ and $K(n)$. Additionally, we prove a density theorem for both $I(n)$ and $K(n)$.

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