On second and eighth order mock theta functions

Cui, Su-Ping; Gu, Nancy S. S.; Hao, Li-Jun

doi:10.1007/s11139-018-0045-4

Cited by 11 publications

(9 citation statements)

References 17 publications

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“…The formula (1.15) was found by Cui, Gu and Hao [17] using Bailey pairs, and (1.17) is due to Gordon and McIntosh [23]. The representation (1.18) appears to be new, and in fact we will show that it is equivalent to (1.17) (see Section 8.5).…”

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confidence: 53%

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Representations of mock theta functions

Chen

Wang

2020

Advances in Mathematics

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Motivated by the works of Liu, we provide a unified approach to find Appell-Lerch series and Hecke-type series representations for mock theta functions. We establish a number of parameterized identities with two parameters a and b. Specializing the choices of (a, b), we not only give various known and new representations for the mock theta functions of orders 2, 3, 5, 6 and 8, but also present many other interesting identities. We find that some mock theta functions of different orders are related to each other, in the sense that their representations can be deduced from the same (a, b)-parameterized identity. Furthermore, we introduce the concept of false Appell-Lerch series. We then express the Appell-Lerch series, false Appell-Lerch series and Hecke-type series in this paper using the building blocks m(x, q, z) and f a,b,c (x, y, q) introduced by Hickerson and Mortenson, as well as m(x, q, z) and f a,b,c (x, y, q) introduced in this paper. We also show the equivalences of our new representations for several mock theta functions and the known representations.

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mentioning

confidence: 53%

“…Using Bailey pairs, Cui, Gu and Hao [17] provided Hecke-type series representations for mock theta functions of order 2. They also express these Hecke-type series in terms of f a,b,c (x, y, q).…”

Section: Mock Theta Functions Of Ordermentioning

confidence: 99%

Representations of mock theta functions

Chen

Wang

2020

Advances in Mathematics

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“…By Theorem 2.4 m(−q 5 z 12 , q 12 , 1/qz 4 ) =m(−q 5 z 12 , q 12 , q 6 /z 12 ) + J 3 12 j(q 5 z 8 ; q 12 )j(−q 2 z 4 ; q 12 ) j(qz 4 ; q 12 )j(q 6 z 12 ; q 12 )j(−q 4 z 8 ; q 12 )j(−q 11 ; q 12 ) , and m(−1/qz 12 , q 12 , qz 4 ) =m(−1/qz 12 , q 12 , q 6 z 12 ) − qz 12 J 3 12 j(q 5 z 8 ; q 12 )j(−q 6 z 4 ; q 12 ) j(qz 4 ; q 12 )j(q 6 z 12 ; q 12 )j(−z 8 ; q 12 )j(−q 5 ; q 12 ) .…”

Section: So That (319)unclassified

“…So that g(z) = g 1 (z) − g 2 (z) where g 1 (z) := zj(qz 4 ; q 2 ) m(−q 5 z 12 , q 12 , q 6 /z 12 ) − 1 q 2 z 8 m(−1/qz 12 , q 12 , q 6 z 12 ) , and g 2 (z) := z 5 J 12 J 2 4 j(−qz 4 ; q 12 ) qJ 8 J 6 j(−z 8 ; q 12 )j(−q 4 z 8 ; q 12 ) J 2 12 J 8 J 2 24 J 4 j(q 14 z 8 ; q 24 ) 2 − q 2 J 2 24 J 6 J 2 4 J 2 12 J 8 J 2 j(q 8 z 8 ; q 12 ) − zJ 3 12 j(qz 4 ; q 2 )j(q 5 z 8 ; q 12 ) j(qz 4 ; q 12 )j(q 6 z 12 ; q 12 ) j(−q 2 z 4 ; q 12 ) j(−q 4 z 8 ; q 12 )j(−q 11 ; q 12 ) + z 4 j(−q 6 z 4 ; q 12 ) qj(−z 8 ; q 12 )j(−q 5 ; q 12 ) .…”

Section: So That (319)unclassified

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

Chen¹,

Chen²

2021

Preprint

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“…We use the following Hecke-type series representation found by Srivastava [44, Eq. (5.4)] and Cui, Gu and Hao [19]:…”

Section: 23)mentioning

confidence: 99%

Parity of coefficients of mock theta functions

Wang

2020

Preprint

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We study the parity of coefficients of classical mock theta functions. Suppose g is a formal power series with integer coefficients, and let c(g; n) be the coefficient of q n in its series expansion. We say that g is of parity type (a, 1 − a) if c(g; n) takes even values with probability a for n ≥ 0. We show that among the 44 classical mock theta functions, 21 of them are of parity type (1, 0). We further conjecture that 19 mock theta functions are of parity type ( 1 2 , 1 2 ) and 4 functions are of parity type ( 3 4 , 1 4 ). We also give characterizations of n such that c(g; n) is odd for the mock theta functions of parity type (1, 0).

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On second and eighth order mock theta functions

Cited by 11 publications

References 17 publications

Representations of mock theta functions

Representations of mock theta functions

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

Parity of coefficients of mock theta functions

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