In this paper, we study the Bochner modular relation (Lambert series) for the kth power of the product of two Riemann zeta-functions with difference (Formula presented.), an integer with the Voronoĭ function weight (Formula presented.). In the case of (Formula presented.), the results reduce to Bochner modular relations, which include the Ramanujan formula, Wigert–Bellman approximate functional equation, and the Ewald expansion. The results abridge analytic number theory and the theory of modular forms in terms of the sum-of-divisor function. We pursue the problem of (approximate) automorphy of the associated Lambert series. The (Formula presented.) case is the divisor function, while the (Formula presented.) case would lead to a proof of automorphy of the Dedekind eta-function à la Ramanujan.