29 citations · 90 across the 22 of their papers we have counts for
25 papers
Hurwitz class number relations and mock modular forms
Kathrin Bringmann, Jia-Wei Guo, Ben Kane +2
A classical class number relation of Hurwitz expresses the Fourier coefficients of the product of a unary theta function and the class number generating function. Here, we establis…
On -congruences for meromorphic modular forms with supersingularity
Kathrin Bringmann, Pavel Guerzhoy, Ben Kane +2
In this paper, we investigate congruences for meromorphic modular forms which have a pole at a single point in the fundamental domain of . For a p…
Class Numbers, Congruent Numbers and Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Michael H. Mertens
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work w…
On Kleinian mock modular forms
Claudia Alfes-Neumann, Michael Mertens
We give an explicit and computationally efficient construction of harmonic weak Maass forms which map to weight newforms under the -operator. Our work uses a new non-analyti…
Hecke eigenforms for meromorphic cusp forms
Kathrin Bringmann, Ben Kane, Michael H. Mertens
In this paper, we construct Hecke eigenforms for two families of quotient spaces of meromorphic cusp forms on . We show that each quotient space in the f…
On Jacobi--Weierstrass mock modular forms
Claudia Alfes-Neumann, Jens Funke, Michael Mertens +1
We construct harmonic weak Maass forms that map to cusp forms of weight with rational coefficients under the -operator. This generalizes work of the first author, Grif…
1-point functions for symmetrized Heisenberg and symmetrized lattice vertex operator algebras
Geoffrey Mason, Michael H. Mertens
We obtain explicit formulas for the -point functions of all states in the symmetrized Heisenberg algebra and symmetrized lattice VOAs . For this we employ a new $\m…
Proof of the elliptic expansion Moonshine Conjecture of Căldăraru, He, and Huang
Letong Hong, Michael H. Mertens, Ken Ono +1
Using predictions in mirror symmetry, Căldăraru, He, and Huang recently formulated a "Moonshine Conjecture at Landau-Ginzburg points" for Klein's modular -function at and…
On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras
Lea Beneish, Michael H. Mertens
Using techniques from the theory of mock modular forms and harmonic Maass forms, especially Weierstrass mock modular forms, we establish several dimension formulas for certain stro…
Mock modular Eisenstein series with Nebentypus
Michael H. Mertens, Ken Ono, Larry Rolen
By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systemati…
Periodicities for Taylor coefficients of half-integral weight modular forms
Pavel Guerzhoy, Michael H. Mertens, Larry Rolen
Congruences of Fourier coefficients of modular forms have long been an object of central study. By comparison, the arithmetic of other expansions of modular forms, in particular Ta…
Modular forms of virtually real-arithmetic type I -- Mixed mock modular forms yield vector-valued modular forms
Michael H. Mertens, Martin Raum
The theory of elliptic modular forms has gained significant momentum from the discovery of relaxed yet well-behaved notions of modularity, such as mock modular forms, higher order…
Pariah moonshine
John F. R. Duncan, Michael H. Mertens, Ken Ono
Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah group…
O'Nan moonshine and arithmetic
John F. R. Duncan, Michael H. Mertens, Ken Ono
Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple gro…
A proof of the Thompson Moonshine Conjecture
Michael J. Griffin, Michael H. Mertens
In this paper we prove the existence of an infinite dimensional graded super-module for the finite sporadic Thompson group whose McKay-Thompson series are weakly holomorphic m…
On the number of parts of integer partitions lying in given residue classes
Olivia Beckwith, Michael Mertens
Improving upon previous work on the subject, we use Wright's Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer that are in any g…
The Number of Parts in Certain Residue Classes of Integer Partitions
Olivia Beckwith, Michael Mertens
We use the Circle Method to derive asymptotic formulas for functions related to the number of parts of partitions in particular residue classes.
Lacunary recurrences for Eisenstein series
Michael H. Mertens, Larry Rolen
Using results from the theory of modular forms, we reprove and extend a result of Romik about lacunary recurrence relations for Eisenstein series.
On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono
Michael H. Mertens, Larry Rolen
Recently, Bruinier and Ono found an algebraic formula for the partition function in terms of traces of singular moduli of a certain non-holomorphic modular function. In this paper…
-adic properties of modular shifted convolution Dirichlet series
Kathrin Bringmann, Michael H. Mertens, Ken Ono
Hoffstein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms and . The second two authors investigated certain s…
Asymptotic formulae for partition ranks
Jehanne Dousse, Michael H. Mertens
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F…
Special values of shifted convolution Dirichlet series
Michael H. Mertens, Ken Ono
In a recent important paper, Hoffstein and Hulse generalized the notion of Rankin-Selberg convolution -functions by defining shifted convolution -functions. We investigate sy…
Eichler-Selberg Type Identities for Mixed Mock Modular Forms
Michael H. Mertens
Using holomorphic projection, we work out a parametrization for all relations of products (resp. Rankin-Cohen brackets) of weight mock modular forms with holomorphic sh…
Mock Modular Forms and Class Number Relations
Michael H. Mertens
In this paper, we prove an almost 40 year old conjecture by H. Cohen concerning the generating function of the Hurwitz class number of quadratic forms using the theory of mock modu…