Eric T. Mortenson
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Eric T. Mortenson has a total of 14 co-authors. Here are the top co-authors by number of shared publications:
- Stepan Konenkov
Department of Mathematics and Computer Science, Saint Petersburg State University, Saint Petersburg, Russia
4 shared publications - Dean Hickerson
Eureka, USA
2 shared publications - Ekaterina Kochetkova
Department of Mathematics and Computer Science, Saint Petersburg State University, Saint Petersburg, Russia
2 shared publications - Mariia Dospolova
St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia
2 shared publications - Ankit Kumar Sahu
Department of Cardiology, Sanjay Gandhi Post Graduate Institute of Medical Sciences, Lucknow, Uttar Pradesh, India
1 shared publication Antun Milas
Department of Mathematics and Statistics, SUNY Albany, Albany, New York 12222, USA
1 shared publication
Latest Publications
- 5 September 2026
- Published by Springer Nature in The Ramanujan Journal
- Vol. 71 (1) , 9
Appell function proofs of recent and old mock theta function identities
- 5 September 2026
- Published by Springer Nature in The Ramanujan Journal
- Vol. 71 (1) , 9
Appell function proofs of recent and old mock theta function identities
- 17 July 2026
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 13 (3) , 62
New polar-finite forms of generalized Euler identities for $A_{1}^{(1)}$-string functions and mock theta conjecture-like identities- 17 July 2026
- Published by Springer Nature in Research in the Mathematical Sciences
- Vol. 13 (3) , 62
New polar-finite forms of generalized Euler identities for $A_{1}^{(1)}$-string functions and mock theta conjecture-like identities- Open Access
New polar-finite forms of generalized Euler identities for $A_{1}^{(1)}$-string functions and mock theta conjecture-like identities
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. For positive admissible-level string functions for the affine Kac--Moody algebra $A_{1}^{(1)}$, very little is known. Here we apply the notion of quasi-periodicity to a generalized Euler identity of Schilling and Warnaar for the affine Kac--Moody algebra $A_{1}^{(1)}$. For integral-level string functions the classical periodicity reduces the infinite sum of string functions in the generalized Euler identity to a finite sum of string functions with theta function coefficients. For admissible-level, we similarly reduce to an analogous finite sum of string functions, but we also gain an additional finite sum of the form \begin{equation*} \sum_{i}Φ_{i}(q)Ψ_{i}(q), \end{equation*} where the $Φ_i(q)$'s are modular and depend only on the spin and the $Ψ_{i}(q)$'s are (mixed) mock modular Hecke-type double-sums and depend only on the quantum number. For levels $1/2$, $1/3$, and $2/3$, we shall also see that the $Ψ_{i}(q)$'s give us families of mock theta conjecture-like identities for symmetric Hecke-type double-sums. Our work here focuses on evaluating the $Ψ_{i}(q)$'s, and our expressions utilize Ramanujan's second-order mock theta function $μ_2(q)$ and third-order mock theta functions $f_{3}(q)$, $ω_3(q)$, $ψ_{3}(q)$, and $χ_3(q)$.Open AccessNew polar-finite forms of generalized Euler identities for $A_{1}^{(1)}$-string functions and mock theta conjecture-like identities
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. For positive admissible-level string functions for the affine Kac--Moody algebra $A_{1}^{(1)}$, very little is known. Here we apply the notion of quasi-periodicity to a generalized Euler identity of Schilling and Warnaar for the affine Kac--Moody algebra $A_{1}^{(1)}$. For integral-level string functions the classical periodicity reduces the infinite sum of string functions in the generalized Euler identity to a finite sum of string functions with theta function coefficients. For admissible-level, we similarly reduce to an analogous finite sum of string functions, but we also gain an additional finite sum of the form \begin{equation*} \sum_{i}Φ_{i}(q)Ψ_{i}(q), \end{equation*} where the $Φ_i(q)$'s are modular and depend only on the spin and the $Ψ_{i}(q)$'s are (mixed) mock modular Hecke-type double-sums and depend only on the quantum number. For levels $1/2$, $1/3$, and $2/3$, we shall also see that the $Ψ_{i}(q)$'s give us families of mock theta conjecture-like identities for symmetric Hecke-type double-sums. Our work here focuses on evaluating the $Ψ_{i}(q)$'s, and our expressions utilize Ramanujan's second-order mock theta function $μ_2(q)$ and third-order mock theta functions $f_{3}(q)$, $ω_3(q)$, $ψ_{3}(q)$, and $χ_3(q)$. - 7 October 2025
- Published by Springer Nature in Research in Number Theory
- Vol. 11 (4) , 1-20
Two 2/5-level mock theta conjecture-like identities
- 7 October 2025
- Published by Springer Nature in Research in Number Theory
- Vol. 11 (4) , 1-20
Two 2/5-level mock theta conjecture-like identities
- 22 August 2025
- Published by Springer Nature in Journal of Mathematical Sciences
- Vol. 292 (2) , 255-265
RAMANUJAN, q-SERIES, AND MOCK THETA FUNCTIONS AT SPbU
- 22 August 2025
- Published by Springer Nature in Journal of Mathematical Sciences
- Vol. 292 (2) , 255-265
RAMANUJAN, q-SERIES, AND MOCK THETA FUNCTIONS AT SPbU
- 18 June 2025
- Published by Springer Nature in The Ramanujan Journal
- Vol. 67 (4) , 1-10
Short proofs of Ramanujan-like identities for the eighth order mock theta function $V_{0}(q)$- 18 June 2025
- Published by Springer Nature in The Ramanujan Journal
- Vol. 67 (4) , 1-10
Short proofs of Ramanujan-like identities for the eighth order mock theta function $V_{0}(q)$- Open Access
Two $2/5$-level mock theta conjecture-like identities
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the explicit forms for fractional-level string functions for the Kac--Moody algebra $A_{1}^{(1)}$. For positive fractional-level string functions they obtained mock theta conjecture-like identities, and for negative fractional-level string functions, they obtained mixed false theta function expressions. Here we find two new families of mock theta conjecture-like identities but for the $2/5$-level string functions. Each of these two families of identities is composed of the four tenth-order mock theta functions from Ramanujan's Lost Notebook as well as a simple quotient of theta functions.Open AccessTwo $2/5$-level mock theta conjecture-like identities
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the explicit forms for fractional-level string functions for the Kac--Moody algebra $A_{1}^{(1)}$. For positive fractional-level string functions they obtained mock theta conjecture-like identities, and for negative fractional-level string functions, they obtained mixed false theta function expressions. Here we find two new families of mock theta conjecture-like identities but for the $2/5$-level string functions. Each of these two families of identities is composed of the four tenth-order mock theta functions from Ramanujan's Lost Notebook as well as a simple quotient of theta functions. - 30 December 2023
- Published by Springer Nature in The Ramanujan Journal
- Vol. 63 (4) , 969-994
A new Andrews–Crandall-type identity and the number of integer solutions to $x^2+2y^2+2z^2=n$- 30 December 2023
- Published by Springer Nature in The Ramanujan Journal
- Vol. 63 (4) , 969-994
A new Andrews–Crandall-type identity and the number of integer solutions to $x^2+2y^2+2z^2=n$- 26 December 2023
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 56 (3) , 1029-1053
On Ramanujan's lost notebook and new tenth‐order like identities for second‐, sixth‐, and eighth‐order mock theta functions
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.
- 26 December 2023
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 56 (3) , 1029-1053
On Ramanujan's lost notebook and new tenth‐order like identities for second‐, sixth‐, and eighth‐order mock theta functions
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.
- Open Access
On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions
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.
Open AccessOn Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions
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.