On Exponential Sums Related to the Circle Problem

On the zeros of a new zeta-function

“…We call zeros ρ of R s; k 4 with β < 1 − C trivial. In [4] it was shown that for any positive integer n…”

“…The function R s; k 4 was introduced in [4],where a truncated Voronoï-type formula for the twisted Möbius transform n x r(n) exp 2πi nk 4…”

“…In [4] it was proved that the function R s; k 4 has an analytic continuation throughout the complex plane except for a simple pole at s = 1, and that it satisfies the functional equation…”