Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Real zeros of Hurwitz-Lerch zeta functions in the interval $(-1,0)$   For $0 < a \le 1$, $s,z \in {\mathbb{C}}$ and $0 < |z|\le 1$, the
Hurwitz-Lerch zeta function is defined by $\Phi (s,a,z) := \sum_{n=0}^\infty
z^n(n+a)^{-s}$ when $\sigma :=\Re (s) >1$. In this paper, we show that $\Phi
(\sigma,a,z) \ne 0$ when $\sigma \in (-1,0)$ if and only if [I] $z=1$ and
$(3-\sqrt{3}) /6 \le a \le 1/2$ or $(3+\sqrt{3}) /6 \le a \le 1$, [II] $z \in
[-1,1)$ and $(1-z)(1-a) \le 1$, [III] $z \not \in {\mathbb{R}}$ and $0<a \le
1$. In addition, we give a new proof of the functional equation of $\Phi
(s,a,z)$.

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The categories of this paper are: nucl-th
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th