A proof of the mod 4 unimodal sequence conjectures and related mock theta functions

  title={A proof of the mod 4 unimodal sequence conjectures and related mock theta functions},
  author={Rong Chen and Frank G. Garvan},
  journal={Advances in Mathematics},

Generating Functions of the Hurwitz Class Numbers Associated with Certain Mock Theta Functions

We find Hecke-Rogers type series representations of generating functions of the Hurwitz class numbers which are similar to certain mock theta functions. We also prove two combinatorial

Bailey pairs and indefinite quadratic forms, II. False indefinite theta functions

  • J. Lovejoy
  • Mathematics
    Research in Number Theory
  • 2022
. We construct families of Bailey pairs ( α n , β n ) where the exponent of q in α n is an indefinite quadratic form, but where the usual ( − 1) j is replaced by a sign function. This leads to

Theta series for quadratic forms of signature (n − 1,1) with (spherical) polynomials

We construct almost holomorphic and holomorphic modular forms by considering theta series for quadratic forms of signature [Formula: see text]. We include homogeneous and spherical polynomials in the

Congruence modulo 4 for Andrews' integer partition with even parts below odd parts

We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of EO(n) and further prove that EO(n) ≡ 0 (mod 4) for almost



Congruences modulo powers of 5 for the rank parity function

International audience It is well known that Ramanujan conjectured congruences modulo powers of 5, 7 and 11 for the partition function. These were subsequently proved by Watson (1938) and Atkin

Unimodal sequences and quantum and mock modular forms

It is shown that the rank generating function U(t; q) for strongly unimodal sequences lies at the interface of quantum modular forms and mock modular forms, and a new representation is obtained for a certain generating function for L-values.

Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers

It is discovered that Ramanujan-type congruences for Hurwitz class numbers can be supported on nonholomorphic generating series and a divisibility result is established for such non holomorphic congruence of Hurwitzclass numbers.

Hecke‐type double sums, Appell–Lerch sums, and mock theta functions, I

By introducing a dual notion between partial theta functions and Appell–Lerch sums, we find and prove a formula which expresses Hecke‐type double sums in terms of Appell–Lerch sums. Not only does our

Odd-balanced unimodal sequences and related functions: parity, mock modularity and quantum modularity

We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In

Torus knots and quantum modular forms

AbstractIn this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2,2t+1). We use this to define a family of

On three third order mock theta functions and Hecke-type double sums

We obtain four Hecke-type double sums for three of Ramanujan’s third order mock theta functions. We discuss how these four are related to the new mock theta functions of Andrews’ work on q-orthogonal


Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5

Universal mock theta functions and two-variable Hecke–Rogers identities

We obtain two-variable Hecke–Rogers identities for three universal mock theta functions. This implies that many of Ramanujan’s mock theta functions, including all the third-order functions, have a