hi... Does anyone have a feeling if the following could plausibly be true? Consider a real valued positive definite matrix $M$. Is the following inequality true?
$$\sum_{k\in\mathbb{Z}^n} e^{-k^T M k} \leq \prod_{i=1}^n \left( \sum_{x \in \mathbb{Z}^n} e^{-\lambda_i x^2} \right) \ .$$
