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math.NT2023★ 2 cited
Exponential sums over Möbius convolutions with applications to partitions
Debmalya Basak, Nicolas Robles, Alexandru Zaharescu
We consider partitions of a positive integer arising from the generating functions \[ \sum_{n=1}^\infty p_{w}(n) z^n = \prod_{m \in \mathbb{N}} (1-z^m)^{-w(m)}, \] w…
math.NT2023
The Riemann zeta function and exact exponential sum identities of divisor functions
Maria Nastasescu, Nicolas Robles, Bogdan Stoica +1
We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existen…