Related papers: Values of twisted Artin $L$-functions

In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.

In this paper we prove that every coefficient of twisted Alexander polynomials of torus knots associated with irreducible $\mathrm{SL}_n(\Bbb C)$-representations is an $\Bbb A$-valued locally constant function on the $\mathrm{SL}_n(\Bbb…

Let $f$ be a fixed holomorphic primitive cusp form of even weight $k$, level $r$ and trivial nebentypus $\chi_r$. Let $q$ be an odd prime with $(q,r)=1$ and let $\chi$ be a primitive Dirichlet character modulus $q$ with $\chi\neq\chi_r$. In…

Let $K/\mathbb Q$ be a finite Galois extension. Let $\chi_1,\ldots,\chi_r$ be $r\geq 1$ distinct characters of the Galois group with the associated Artin L-functions $L(s,\chi_1),\ldots, L(s,\chi_r)$. Let $m\geq 0$. We prove that the…

We prove an existence result for twisted K\"ahler-Einstein metrics, assuming an appropriate twisted K-stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed.

Under the Generalized Riemann Hypothesis, we prove that given any two distinct imprimitive Dirichlet characters $\eta_1, \eta_2$ modulo $q=p^k$, a positive proportion of characters $\chi$ modulo $q$ in a fixed Galois orbit of primitive…

Let $L(s,\chi)$ be a fixed Dirichlet $L$-function. Given a vertical arithmetic progression of $T$ points on the line $\Re(s)=1/2$, we show that $\gg T \log T$ of them are not zeros of $L(s,\chi)$. This result provides some theoretical…

Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_\Gamma$…

Consider central $L$-values of even weight elliptic or Hilbert modular forms $f$ twisted by ideal class characters $\chi$ of an imaginary quadratic extension $K$. Fixing $\chi$, and assuming $K$ is inert at each prime dividing the level,…

A susceptibility function ${\chi}(L)$ is introduced to quantify some aspects of the intermittent stick-slip dynamics of a rough metallic cylinder of length $L$ on a rough metallic incline submitted to small controlled perturbations and…

We study the one-level density for families of L-functions associated with cubic Dirichlet characters defined over the Eisenstein field. We show that the family of $L$-functions associated with the cubic residue symbols $\chi_n$ with $n$…

"Murmurations" are a recently-discovered type of fine structure in sums of Dirichlet coefficients averaged over families of $L$-functions. The root cause of this phenomenon remains mysterious. In the present paper, we demonstrate how…

In this article, we systematically investigate the stability properties of certain warped product Einstein manifolds. We characterize stability of these metrics in terms of an eigenvalue condition of the Einstein operator on the base…

We present a simple analytic proof that L-functions of real non-principal Dirichlet characters are nonzero at 1.

Let $\psi$ be a real primitive character modulo $D$. If the $L$-function $L(s,\psi)$ has a real zero close to $s=1$, known as a Landau-Siegel zero, then we say the character $\psi$ is exceptional. Under the hypothesis that such exceptional…

We establish an asymptotic formula for the first moment and derive an upper bound for the second moment of L-functions associated with the complete family of primitive cubic Dirichlet characters defined over the Eisenstein field. Our…

We study a double Dirichlet series of the form $\sum_{d}L(s,\chi_{d}\chi)\chi'(d)d^{-w}$, where $\chi$ and $\chi'$ are quadratic Dirichlet characters with prime conductors $N$ and $M$ respectively. A functional equation group isomorphic to…

In this paper, we prove hybrid subconvexity bounds for $\rm GL_2\times \rm GL_2$ Rankin--Selberg $L$-functions twisted by a primitive Dirichlet character $\chi$ modulo a prime power, in the $t$ and depth aspects.

Let $\chi$ a primitive character$\pmod q$ and consider the Dirichlet $L$-function $$L(s,\chi)=\sum_{n=1}^{\infty}\frac{\chi(n)}{n^s}.$$ We give a new proof of an upper bound of Heath-Brown for $|L(s,\chi)|$ on the critical line $s=1/2+it$

Let $X$ be an orbisurface, meaning a compact hyperbolic Riemann surface possibly with a finite number of elliptic points, and let $X_1$ denote its unit tangent bundle. We consider the twisted Selberg zeta function $Z(s;\rho)$ associated to…