Zeta functions of alternate mirror Calabi-Yau families

Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces

“…The main aim of this paper is to generalize and to comment on a recent result of Doran, Kelly, Salerno, Sperber, Voight and Whitcher [8] on the zeta function of certain pencils of Calabi-Yau hypersurfaces. For a more extensive discussion on the history of this particular result we refer to the introduction of [8].…”

“…In a recent preprint Doran, Kelly, Salerno, Sperber, Voight and Whitcher [8] showed the following result (using Dwork cohomology and some results on the Picard-Fuchs equation):…”

“…To describe the main results from [8], fix a matrix A := (a i,j ) 0≤i,j≤n with nonnegative integral coefficients and nonzero determinant. Then with A we can associate the polynomial…”

“…. , 1)A −1 is the same as the condition dual weights being equal from the paper [8], whenever the latter condition is defined.…”

Supercongruences Occurred to Rigid Hypergeometric Type Calabi–Yau Threefolds

“…We list the corresponding maps in Table 5; as they are not uniquesome instances differ from the descriptions in other sources, for example, in [12]. In the literature, there are many papers on counting the number of solutions of these algebraic equations of type (37) over finite fields; see, e.g., [18,26,27,45,55]. In particular, it is shown in [55] that V α (ψ) and its mirror V α (λ) share the same unit root.…”