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Abstract:
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The subject of the dissertation is the problem of simultaneous nonvanishing
of quadratic twists of elliptic curve 𝐿-functions and quadratic Dirichlet 𝐿-functions (and
their derivatives) at the centar point 𝑠 =
1
2
, in the situation when these objects are
defined over the rational function field over finite field F𝑞.
For each monic polynomial 𝐷 ∈ F𝑞 [𝑡], there is a corresponding quadratic Dirichlet
character 𝜒𝐷. Associated to such character, there is the corresponding Dirichlet 𝐿-
function 𝐿(𝑠, 𝜒𝐷), as well as the quadratic twist 𝐸 ⊗ 𝜒𝐷 of a fixed elliptic curve 𝐸/F𝑞 (𝑡),
whose 𝐿-function is denoted by 𝐿(𝑠, 𝐸 ⊗ 𝜒𝐷).
A lower bound for the number of polynomials 𝐷 ∈ H∗
2𝑔+1
such that 𝐿 |