Related papers: Godement-Jacquet $L$-function, some conjectures an…

In this paper, we consider the $k$-th Riesz mean for the coefficients of the Rankin-Selberg $L$-function $L_{f \times f}(s)$ related to the Godement-Jacquet $L$-function with respect to $SL(n,\mathbb{Z})$. We establish an asymptotic formula…

The GUE Hypothesis, which concerns the distribution of zeros of the Riemann zeta-function, is used to evaluate some integrals involving the logarithmic derivative of the zeta-function. Some connections are shown between the GUE Hypothesis…

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…

In this series, we investigate the calculation of mean values of derivatives of Dirichlet $L$-functions in function fields using the analogue of the approximate functional equation and the Riemann Hypothesis for curves over finite fields.…

We develope the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic Hecke $L$-functions in the Gaussian field using multiple Dirichlet series under the generalized…

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

Assuming the generalized Lindel\"{o}f hypothesis (GLH), a weak version of the generalized Ramanujan conjecture and a Rankin--Selberg type partial sum estimate, we establish the normality of the sum of coefficients of a general $L$-function…

Let $f$ be a holomorphic cusp form of weight $k$ with respect to full modular group $SL_2(\mathbb{Z})$ satisfying a normalized Hecke eigenform, $L_f(s)$ the $L$-function attached to the form $f$. Good gave the approximate functional…

Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic families of Dirichlet and Hecke L-functions of primerelated moduli…

We formulate a general conjecture relating Chern classes of subbundles of Gauss-Manin bundles in Arakelov geometry to logarithmic derivatives of Artin L-functions of number fields. This conjecture may be viewed as a far-reaching…

We apply the method of multiple Dirichlet series to develop $L$-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of quartic Hecke $L$-functions of prime moduli over the…

We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the…

Assuming the generalized Riemann hypothesis and a bound for the negative discrete moments of the Riemann zeta function (resp. Dirichlet $L$-functions), we prove the existence of a logarithmic limiting distribution for the normalized partial…

In this paper, we will give estimates for the logarithmic derivative $ \left\vert \frac{f^{\left( k\right) }\left( z\right) }{f\left( z\right) } \right\vert $ where $f$ is a meromorphic function in a region of the form $ D\left( 0,R\right)…

We relate poles of local Godement-Jacquet L-functions to distributions on matrix spaces with singular supports. As an application, we show the irreducibility of the full theta lifts to $GL_n(F)$ of generic irreducible representations of…

We present an elementary derivation of the Jacquet-Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients $A(m_1,...,m_{n-1})$.

In this paper various analytic techniques are com- bined in order to study the average of a product of a Hecke L- function and a symmetric square L-function at the central point in the weight aspect. The evaluation of the second main term…

For univalent and normalized functions $f$ the logarithmic coefficients $\gamma_n(f)$ are determined by the formula $\log(f(z)/z)=\sum_{n=1}^{\infty}2\gamma_n(f)z^n$. In the paper \cite{Pon} the authors posed the conjecture that a locally…

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…

In this paper, we establish joint extreme values of Dirichlet (L)-functions and their logarithmic derivatives using the resonance method. Our results extend previous work of Aistleitner et al. (2019) and Yang (2023).