On the Conditional Bounds for Siegel Zeros

On the Landau-Siegel Zeros Conjecture

Some Remarks on Landau-siegel Zeros

In this paper we show that, under the assumption that all the zeros of the L-functions under consideration are either real or lie on the critical line, one may considerably improve on the known results on Landau-Siegel zeros.

Siegel zeros of Eisenstein series

(m,n)6=(0,0) y |mz+n|2s is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z, s) has a ”Siegel zero.” That is E(z, β) = 0 for a real number β just to the left of one. We give a generalization of this result to Eisenstein series formed with real valued automorphic forms on a finite central covering of the adele points of a connected reductive al...

Bounds for Zeros of the Charlier Polynomials

We use the method of positive quadratic forms and discrete analogues of the Laguerre inequality recently obtained by the author, to give bounds on the zeros of the Charlier polynomials, which are uniform in all parameters involved.

On Bounds For The Zeros of Univariate Polynomials

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated. Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds fo...