Related papers: Two-ends Furstenberg estimates in the plane
The dominated convergence theorem implies that if (f_n) is a sequence of functions on a probability space taking values in the interval [0,1], and (f_n) converges pointwise a.e., then the sequence of integrals converges to the integral of…
We consider iterated integrals of $\log\zeta(s)$ on certain vertical and horizontal lines. Here, the function $\zeta(s)$ is the Riemann zeta-function. It is a well known open problem whether or not the values of the Riemann zeta-function on…
We establish Kronecker limit type formula for the generalized Mordell-Tornheim zeta function $\Theta(r,r,t,x)$ as a function of the third argument around $t=1-r$. We then show that the above Kronecker limit type formula is equivalent to the…
Guth and Katz proved that any point set $\mathcal P$ in the plane determines $\Omega(|\mathcal P|/\log|\mathcal P|)$ distinct distances. We show that when near to this lower bound, a point set $\mathcal P$ of the form $A\times A$ must…
We establish improved bounds for bilinear forms with Kloosterman fractions of the form ${\sum\sum}_{m,n} \alpha_m \beta_n e(a\overline{m}/(bn))$ with $M<m\le 2M$, $N < n \le 2N$ and $(m,n)=1$. Our approach works directly with arbitrary…
We first survey the known results on functional equations for the double zeta-function of Euler type and its various generalizations. Then we prove two new functional equations for double series of Euler-Hurwitz-Barnes type with complex…
Using a characterization of parabolics in reductive Lie groups due to Furstenberg, elementary properties of buildings, and some algebraic topology, we give a new proof of Tits' classification of 2-transitive Lie groups.
We establish two direct extensions to the Butterfly Theorem on the cyclic quadrilateral along with the proofs using the projective method and analytic geometry of the Cartesian coordinate system.
This article improves the estimate of $|S_1(t_2)-S_1(t_1)|$, which is the definite integral of the argument of the Riemann zeta-function between $t_1$ and $t_2$. Estimates of this quantity are needed to apply Turing's method to compute the…
We establish a generalized Cassels-Tate dual exact sequence for 1-motives over global fields. We thereby extend the main theorem of [4] from abelian varieties to arbitrary 1-motives.
In this paper we obtain sharp weighted estimates for solutions of the $\partial$-equation in a lineally convex domains of finite type. Precisely we obtain estimates in spaces of the form L p ({\Omega},$\delta$ $\gamma$), $\delta$ being the…
Building on a result by Tao, we show that a certain type of simple closed curve in the plane given by the union of the graphs of two $1$-Lipschitz functions inscribes a square whose sidelength is bounded from below by a universal constant…
Two integral representations of q-analogues of the Hurwitz zeta function are established. Each integral representation allows us to obtain an analytic continuation including also a full description of poles and special values at…
We prove a result on approximations to a real number $\theta$ by algebraic numbers of degree $\le 2$ in the case when we have information about the uniform Diophantine exponent $\hat{\omega}$ for the linear form $x_0 +\theta…
A method of ``algebraic estimates'' is developed, and used to study the stability properties of integrals of the form \int_B|f(z)|^{-\d}dV, under small deformations of the function f. The estimates are described in terms of a stratification…
We generalize a result of Ruzsa on the inverse Erdos-Fuchs theorem for k-fold sumsets.
A weighted area estimate for entire graphs with bounded weighted mean curvature in Gauss space is given by a simple proof. Bernstein type theorems for self shrinkers (\cite {wa}) as well as for graphic $\lambda$-hypersurfaces (\cite{…
We study graphs coming from quadratic spaces over finite fields via orthogonality which generalize a recent result given by Bishnoi, Ihringer, and Pepe (2019). More precisely, we study the graph $\Gamma^{\square}(n,k,q)$ as follows: the…
The vertical Sato--Tate conjectures gives expected trace distributions for for families of curves. We develop exact expression for the distribution associated to degree-$4$ representations of $\mathrm{USp}(4)$,…
In this paper, we study the explicit expressions of multiple t-star values with an arbitrary number of blocks of twos of general level. We give an expression of a generating function of such values, which generalizes the results for…