Baker’s conjecture and Eremenko’s conjecture for functions with negative zeros

A bound for Feichtinger conjecture

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...

On the Landau-Siegel Zeros Conjecture

Real entire functions with real zeros and a conjecture of Wiman

This conclusion is not true for the first derivative as the example exp(sin z) shows. For real entire functions with finitely many zeros, all of them real, Theorem 1.1 was proved in [3]. Theorem 1.1 can be considered as an extension to functions of infinite order of the following result of Sheil-Small [20], conjectured by Wiman in 1914 [1, 2]. For every integer p ≥ 0, denote by V2p the set of e...

The Auslander-Reiten Conjecture for Group Rings

This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...

Sensitivity Conjecture and Log-Rank Conjecture for Functions with Small Alternating Numbers

The Sensitivity Conjecture and the Log-rank Conjecture are among the most important and challenging problems in concrete complexity. Incidentally, the Sensitivity Conjecture is known to hold for monotone functions, and so is the Log-rank Conjecture for f(x∧y) and f(x⊕y) with monotone functions f , where ∧ and ⊕ are bit-wise AND and XOR, respectively. In this paper, we extend these results to fu...