Zeros of Lattice Sums Zeros of Epstein Zeta Functions off the Critical Line
نویسنده
چکیده
We consider zeros of two-dimensional sums over rectangular lattices, and in particular a sum first studied by Potter and Titchmarsh in 1935. They proved several properties of the zeros of sums over the rectangular lattice, and commented on the fact that a particular sum had zeros off the critical line. We investigate the behaviour of one such zero as a function of the ratio of the periods of the rectangular lattice, and show that it evolves continuously along a trajectory which approaches the critical line, reaching it at a point which is a second-order zero of the rectangular lattice sum.
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