Related papers: Multiple standard twists of $L$-functions

We try to understand the poles of L-functions via taking a limit in a trace formula. This technique avoids endoscopic and Kim-Shahidi methods. In particular, we investigate the poles of the Rankin-Selberg L-function. Using analytic number…

The edge-of-the-wedge theorem in several complex variables gives the analytic continuation of functions defined on the poly upper half plane and the poly lower half plane, the set of points in $\mathbb{C}^d$ with all coordinates in the…

For a wide class of Dirichlet series associated to automorphic forms, we show that those without Euler products must have zeros within the region of absolute convergence. For instance, we prove that if f is a classical holomorphic modular…

Let D be a bounded domain in the complex plane whose boundary bD consists of finitely many pairwise disjoint real analytic simple closed curves. Let f be an integrable function on bD. In the paper we show how to compute the candidates for…

We prove that the Dirichlet $L$-functions associated with Dirichlet characters in $\mathbb{F}_{q}[x]$ are universal. That is, given a modulus of high enough degree, $L$-functions with characters to this modulus can be found that approximate…

In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple…

Let X be a smooth projective curve over a finite field. We describe H, the full Hall algebra of vector bundles X as a Feigin-Odesskii shuffle algebra. This shuffle algebra corresponds to the scheme S of all cusp eigenforms and to the…

We characterize those algebras over a disconnected uniformly complete topological field which are representable as algebras of continuous functions on compact topological spaces, generalizing thus Gelfand duality for non-archimedean normed…

In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire $L$-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet…

We provide the full theory of thermodynamic formalism for a very general collection of entire functions in class $\mathcal B$. This class overlaps with the collection of all entire functions for which thermodynamic formalism has been so far…

We achieve the multifractal analysis of a class of complex valued statistically self-similar continuous functions. For we use multifractal formalisms associated with pointwise oscillation exponents of all orders. Our study exhibits new…

We show that there exist constants $\alpha,\epsilon>0$ such that for every positive integer $n$ there is a continuous odd function $f:S^m\to S^n$, with $m\geq \alpha n$, such that the $\epsilon$-expansion of the image of $f$ does not…

We investigate a relation between the Mordell-Tornheim type of multiple Dirichlet series and a confluent hypergeometric function. We prove it by applying the Mellin-Barnes integral formula. Also, main results in this paper contain two kinds…

We define two $L$-functions associated to a common vector valued eigenform $f$ transforming with the ``finite'' Weil representation. The first one can be seen as a standard zeta function defined by the eigenvalues of $f$. The second one can…

We consider modular functions (i.e., the Eisenstein series and Hecke-Maass forms) for the group PSL(2,Z). We fix a quadratic number field E. This gives rise to twisted (by a Hecke character of the field E) periods of a modular function…

For $d > 1$ a cubefree rational integer, we define an $L$-function (denoted $L_d(s)$) whose coefficients are derived from the cubic theta function for $\mathbb Q\left(\sqrt{-3}\right)$. The Dirichlet series defining $L_d(s)$ converges for…

We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function, namely, that it cannot be covered by countably many sets, each of which is closed and purely…

For a holomorphic function f on a complex manifold M we explain in this article that the distribution associated to |f | 2$\alpha$ (Log|f | 2) q f --N by taking the corresponding limit on the sets {|f | $\ge$ $\epsilon$} when $\epsilon$…

Dimensions of level sets of generic continuous functions and generic H\"older functions defined on a fractal $F$ encode information about the geometry, ``the thickness" of $F$. While in the continuous case this quantity is related to a…

Let $f$ be an entire function and $L(f)$ a linear differential polynomial in $f$ with constant coefficients. Suppose that $f$, $f'$, and $L(f)$ share a meromorphic function $\alpha(z)$ that is a small function with respect to $f$. A…