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On certain explicit congruences for mock theta functions
Recently, Garthwaite and Penniston have shown that the coefficients of Ramanujan's mock theta function ω satisfy infinitely many congruences of Ramanujan type. In this work we give the first explicitExpand
Equivalence Problems for Circuits over Sets of Natural Numbers
TLDR
This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪,∩,−,+,×}-circuits. Expand
Satisfiability of algebraic circuits over sets of natural numbers
TLDR
This work proves that testing satisfiability for {@?,+,x}-circuits is already undecidable, and shows that satisfiability problems capture a wide range of complexity classes such as NL, P, NP, PSPACE, and beyond. Expand
Satisfiability of Algebraic Circuits over Sets of Natural Numbers
TLDR
It is proved that testing satisfiability for {∩, +, ×}- circuits already is undecidable, and that in several cases, satisfiability problems are harder than membership problems. Expand
Equivalence Problems for Circuits over Sets of Natural Numbers
TLDR
This work gives a systematic characterization of the complexity of equivalence problems over sets of natural numbers and provides an improved upper bound for the case of {∪, ∩,-,+, ×}-circuits. Expand
ASYMPTOTICS FOR MOMENTS OF HIGHER RANKS
Bringmann, Mahlburg, and Rhoades have found asymptotic expressions for all moments of the partition statistics rank and crank. In this work we extend their methods to higher ranks. The T-rank,Expand
A MAASS LIFTING OF Θ 3 AND CLASS NUMBERS OF REAL AND IMAGINARY QUADRATIC FIELDS
We give an explicit construct of a harmonic weak Maass form FΘ that is a “lift” of Θ3, where Θ is the classical Jacobi theta function. Just as the Fourier coefficients of Θ3 are related to classExpand
Congruences for the Fourier coefficients of the Mathieu mock theta function
Abstract In this paper, we study the congruences for the Fourier coefficients of the Mathieu mock theta function, which appears in the Mathieu moonshine phenomenon discovered by Eguchi, Ooguri, andExpand
Explicit congruences for mock modular forms
In recent work of Bringmann, Guerzhoy, and the first author, p-adic modular forms were constructed from mock modular forms. This paper proves explicit congruences for these p-adic modular forms.
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