Related papers: On the conditional bounds for Siegel zeros

In this paper, we prove the weak Siegel-Weil formula for the space M_2(Q) . We study the Hecke correspondence and representation numbers associated to Eichler orders, and give the explicit formula for degree of Hecke correspondence and…

In this note, we consider Szemer\'{e}di's theorem on $k$-term arithmetic progressions over finite fields $\mathbb{F}_p^n$, where the allowed set $S$ of common differences in these progressions is chosen randomly of fixed size. Combining a…

We establish a new version of Siegel's lemma over a number field $k$, providing a bound on the maximum of heights of basis vectors of a subspace of $k^N$, $N \geq 2$. In addition to the small-height property, the basis vectors we obtain…

In this paper, we investigate the chiral boundary value problem for the Landau-Lifshitz equation with helical derivatives. By introducing Sobolev spaces adapted to the helical derivative and establishing energy estimates that are compatible…

According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results…

The work of Chatzidakis and Hrushovski on the model theory of difference fields in characteristic zero showed that groups defined by difference equations have a very restricted structure. Recent work of Chatzidakis, Hrushovski and Peterzil…

This is the first in a series of papers on type I Howe duality for finite fields, concerning the restriction of an oscillator representation of the symplectic group to a product of a symplectic and an orthogonal group. The goal of the…

We state four open problems on Iwahori-Hecke algebras. The first one states a relation between some algebras appearing in Solleveld's work and some explicit Hecke algebras appearing in the study of unipotent representations. The second one…

The cardinal invariants $ \mathfrak h, \mathfrak b, \mathfrak s$ of $\mathcal P (\omega)$ are known to satisfy that $\omega_1 \leq \mathfrak h \leq\min\{\mathfrak b, \mathfrak s\}$. We prove that all inequalities can be strict. We also…

We extend the Brauer-Siegel theorem to new families of number fields, both in the classical setting of asymptotically bad families and in the more general framework due to Tsfasman and Vl\u{a}du\c{t} of asymptotically exact families. We…

We show the invalidity of finitary counterparts for three classification theorems: The preservation of being a Bernoulli shift through factors, Sinai's factor theorem, and the weak Pinsker property. We construct a finitary factor of an…

For a number field $k$ and an odd prime $p$, let $\tilde{k}$ be the compositum of all the ${\mathbb Z}_p$-extensions of $k$, $\tilde{\Lambda }$ the associated Iwasawa algebra, and $X(\tilde{k})$ the Galois group over $\tilde{k}$ of the…

Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate…

The first Szego limit theorem has been extended by Bump-Diaconis and Tracy-Widom to limits of other minors of Toeplitz matrices. We extend their results still further to allow more general measures and more general determinants. We also…

By providing a variant of Weyl's inequality for general systems of forms we establish the Hardy-Littlewood asymptotic formula for the density of integer zeros of systems of quadratic or cubics forms under weaker rank conditions than…

Recently, Dixit et al. established a very elegant generalization of Hardy's Theorem concerning the infinitude of zeros that the Riemann zeta function possesses at its critical line. By introducing a general transformation formula for the…

In this article, we obtain new results for Fourier restriction type problems on compact Lie groups. We first provide a sharp form of $L^p$ estimates of irreducible characters in terms of their Laplace-Beltrami eigenvalue and as a…

Following N. Elkies ("ABC implies Mordell") we show that the abc conjecture of Masser-Oesterle implies an effective version of Siegel's theorem about integral points on algebraic curves, i.e. an upper bound for the S-integral points where…

Ortega-Cerd\`a -- Seip demonstrated that there are bounded multiplicative Hankel forms which do not arise from bounded symbols. On the other hand, when such a form is in the Hilbert-Schmidt class $\mathcal{S}_2$, Helson showed that it has a…

In this paper, we introduce the zero divisor graph of a multiplicative lattice. We provide a counter example to Beck's conjecture for multiplicative lattices. Further, we prove that Beck's conjecture is true for reduced multiplicative…