Andreas Weingartner

Zeros of Dirichlet series with periodic coefficients

Let

On the degrees of polynomial divisors over finite fields

a=(a_n)_{n\ge 1}

On integers

be a periodic sequence,

n

F_a(s)

for which

the meromorphic continuation of

X^n-1

\sum_{n\ge 1} a_n/n^s

has a divisor of every degree

, and

An explicit polynomial analogue of Romanoff's theorem

N_a(\sigma_1, \sigma_2, T)

Piatetski-Shapiro sequences

the number of zeros of

PRACTICAL NUMBERS AND THE DISTRIBUTION OF DIVISORS

F_a(s)