The highest lowest zero of general L-functions

The Highest - Lowest Zero and otherAppli ations

The Highest-Lowest Zero and other Applications of Positivity

The first nontrivial zeroes of the Riemann ζ function are ≈ 1 2 ± 14.13472i. We investigate the question of whether or not any other Lfunction has a higher lowest zero. To do so we try to quantify the notion that the L-function of a “small” automorphic representation (i.e. one with small level and archimedean type) does not have small zeroes, and vice-versa. We prove that many types of automorp...

Zero Spacing Distributions for Differenced L-Functions

The paper studies the local zero spacings of deformations of the Riemann ξ-function under certain averaging and differencing operations. For real h we consider the entire functions Ah(s) := 1 2 (ξ(s + h) + ξ(s− h)) and Bh(s) = 1 2i (ξ(s+ h)− ξ(s− h)) . For |h| ≥ 1 2 the zeros of Ah(s) and Bh(s) all lie on the critical line R(s) = 1 2 and are simple zeros. The number of zeros of these functions ...

the relationship between academic self-concept and academic achievement in english and general subjects of the students of high school

according to research, academic self-concept and academic achievement are mutually interdependent. in the present study, the aim was to determine the relationship between the academic self-concept and the academic achievement of students in english as a foreign language and general subjects. the participants were 320 students studying in 4th grade of high school in three cities of noor, nowshah...

An Explicit Zero-free Region for the Dirichlet L-functions

Let Lq(s) be the product of Dirichlet L-functions modulo q. Then Lq(s) has at most one zero in the region Rs ≥ 1− 1 6.3970 logmax(q, q|Is|) .