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19 papers · 1 filter
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…
Zeros of Rankin-Selberg -functions in families
Peter Humphries, Jesse Thorner
Let be the set of all cuspidal automorphic representations of with unitary central character over a number field . We prove the first uncond…
Complexity of Leading Digit Sequences
Xinwei He, A. J. Hildebrand, Yuchen Li +1
Let denote the sequence of leading digits of in base . It is well known that if is not a rational power of , then the sequence satisfies Benford…
A polyharmonic Maass form of depth 3/2 for SL_2(Z)
Scott Ahlgren, Nickolas Andersen, Detchat Samart
Duke, Imamoglu, and Toth constructed a polyharmonic Maass form of level 4 whose Fourier coefficients encode real quadratic class numbers. A more general construction of such forms…
Moments of averages of generalized Ramanujan sums
Nicolas Robles, Arindam Roy
Let be a positive integer. A generalization of the Ramanujan sum due to Cohen is given by \begin{align} c_{q,β}(n) := \sum\limits_{{{(h,{q^β})}_β} = 1} {e^{2πinh/{q^β}}}, \nonu…
Euler-like recurrences for smallest parts functions
Scott Ahlgren, Nickolas Andersen
We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holom…