Zero distribution of Dirichlet L-functions

Abstract

Abstract. In this paper, we point out that there exists a positive percentage of the simple a-points of L χ for a complex number a. Furthermore, we establish some inequalities about the number of distinct zeros of Dirichlet L-functions employing value distribution theory and other analytic tools.

A study on value distribution of the Riemann zeta function

“…In view of f (s) and ζ(s) satisfy the same functional equation, therefore (15) also shows that all the trivial zeros of ζ(s) with finitely many exceptions are the roots of equation…”

“…Recently, the problem has been generalized from the Riemann zeta-function to certain L-function, see eg. monograph [15], [24].…”

Semi-algebraic properties of Minkowski sums of a twisted cubic segment

“…3,n is contained in B + n ∪ B − n by Lemma 5.4 and we know that the projection maps B + n → B n , (x, y, z) → (x, y), and B − n → B n , (x, y, z) → (x, y), are bijections by Propositions 6.1 and 6.2. Together these statements imply (a).…”

“…The zeros of L-functions are known to be able to describe various geometrical and arithmetical objects and are the subjects of several conjectures (cf. [1][2][3]). For example, the Generalized Riemann Hypothesis conjectures that all non-trivial zeros of an L-function have real part 1 2 and the Grand Simplicity Hypothesis asserts that the imaginary parts of zeros of Dirichlet L-functions are linearly independent over Q (cf.…”