On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions

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On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions. / Mortenson, Eric T.

в: Bulletin of the London Mathematical Society, Том 56, № 3, 01.03.2024, стр. 1029-1053.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{0722f533f17c47f9b731d901fd166021,

title = "On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions",

abstract = "Ramanujan's lost notebook contains many mock theta functions and mock theta function identities not mentioned in his last letter to Hardy. For example, we find the four tenth-order mock theta functions and their six identities. The six identities themselves are of a spectacular nature and were first proved by Choi. We also find eight sixth-order mock theta functions in the lost notebook, but among their many identities there is only a single relationship like those of the tenth-orders. Using Appell function properties of Hickerson and Mortenson, we discover and prove three new identities for the sixth-order mock theta functions that are in the spirit of the six tenth-order identities. We also include an additional nineteen tenth-order like identities for various combinations of second-, sixth-, and eighth-order mock theta functions.",

author = "Mortenson, {Eric T.}",

year = "2024",

month = mar,

day = "1",

doi = "10.1112/blms.12980",

language = "English",

volume = "56",

pages = "1029--1053",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "Oxford University Press",

number = "3",

}

RIS

TY - JOUR

T1 - On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions

AU - Mortenson, Eric T.

PY - 2024/3/1

Y1 - 2024/3/1

N2 - Ramanujan's lost notebook contains many mock theta functions and mock theta function identities not mentioned in his last letter to Hardy. For example, we find the four tenth-order mock theta functions and their six identities. The six identities themselves are of a spectacular nature and were first proved by Choi. We also find eight sixth-order mock theta functions in the lost notebook, but among their many identities there is only a single relationship like those of the tenth-orders. Using Appell function properties of Hickerson and Mortenson, we discover and prove three new identities for the sixth-order mock theta functions that are in the spirit of the six tenth-order identities. We also include an additional nineteen tenth-order like identities for various combinations of second-, sixth-, and eighth-order mock theta functions.

AB - Ramanujan's lost notebook contains many mock theta functions and mock theta function identities not mentioned in his last letter to Hardy. For example, we find the four tenth-order mock theta functions and their six identities. The six identities themselves are of a spectacular nature and were first proved by Choi. We also find eight sixth-order mock theta functions in the lost notebook, but among their many identities there is only a single relationship like those of the tenth-orders. Using Appell function properties of Hickerson and Mortenson, we discover and prove three new identities for the sixth-order mock theta functions that are in the spirit of the six tenth-order identities. We also include an additional nineteen tenth-order like identities for various combinations of second-, sixth-, and eighth-order mock theta functions.

UR - https://www.mendeley.com/catalogue/269482bb-99e8-3a42-8194-33caca122a6b/

U2 - 10.1112/blms.12980

DO - 10.1112/blms.12980

M3 - Article

VL - 56

SP - 1029

EP - 1053

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 3

ER -

ID: 126318113