### Partition Analysis [SFB F050-06]

Project Lead: Peter Paule

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# Dr. Liangjie Ye

### Research Area

analytic number theory, special functions## Ongoing Projects

### Partition Analysis [SFB F050-06]

Project Duration: 01/03/2013 - 31/07/2022MoreProject Website### Computer Algebra Tools for Special Functions [DK6]

Project Duration: 01/10/2011 - 30/06/2022MoreProject Website## Publications

All 2022 - 2020 2019 - 2017 2016 - 2014 2013 - 2011 2010 - 2008 2007 - 2005 2004 - 2002 2001 - 1999 1998 - 1996 1995 - 1993 1992 - 1990 1989 - 1987 1986 - 1965 ### 2019

### The Generators of all Polynomial Relations among Jacobi Theta Functions

#### Ralf Hemmecke, Silviu Radu, Liangjie Ye

In: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, Johannes Blümlein and Carsten Schneider and Peter Paule (ed.), Texts & Monographs in Symbolic Computation 18-09, pp. 259-268. 2019. Springer International Publishing, Cham, 978-3-030-04479-4. Also available as RISC Report 18-09 http://www.risc.jku.at/publications/download/risc_5719/thetarelations.pdf. [doi]
### 2017

### Elliptic Function Based Algorithms to Prove Jacobi Theta Function Relations

#### Liangjie Ye

Journal of Symbolic Computation, to appear, pp. 1-25. 2017. -. [pdf]
### A Symbolic Decision Procedure for Relations Arising among Taylor Coefficients of Classical Jacobi Theta Functions

#### Liangjie Ye

Journal of Symbolic Computation 82, pp. 134-163. 2017. ISSN: 0747-7171. [pdf]
### Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities

#### Liangjie Ye

RISC and the DK program Linz. PhD Thesis. 2017. Updated version in June 2017. [pdf]
### 2011

### Lower Bounds and Constructions for q-ary Codes Correcting Asymmetric Errors

#### Qunying Liao, Liangjie Ye

Advances in Mathematics(China) 42(6), pp. 795-800. 2011. ISSN:1000-0917 . [url] [pdf]

Project Lead: Peter Paule

Project Lead: Peter Paule

[Ye]

@**incollection**{RISC5913,

author = {Ralf Hemmecke and Silviu Radu and Liangjie Ye},

title = {{The Generators of all Polynomial Relations among Jacobi Theta Functions}},

booktitle = {{Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}},

language = {english},

abstract = {In this article, we consider the classical Jacobi theta functions$\theta_i(z)$, $i=1,2,3,4$ and show that the ideal of all polynomialrelations among them with coefficients in$K :=\setQ(\theta_2(0|\tau),\theta_3(0|\tau),\theta_4(0|\tau))$ isgenerated by just two polynomials, that correspond to well knownidentities among Jacobi theta functions.},

series = {Texts & Monographs in Symbolic Computation},

number = {18-09},

pages = {259--268},

publisher = {Springer International Publishing},

address = {Cham},

isbn_issn = {978-3-030-04479-4},

year = {2019},

note = {Also available as RISC Report 18-09 http://www.risc.jku.at/publications/download/risc_5719/thetarelations.pdf},

editor = {Johannes Blümlein and Carsten Schneider and Peter Paule},

refereed = {yes},

length = {9},

url = {https://doi.org/10.1007/978-3-030-04480-0_11}

}

author = {Ralf Hemmecke and Silviu Radu and Liangjie Ye},

title = {{The Generators of all Polynomial Relations among Jacobi Theta Functions}},

booktitle = {{Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}},

language = {english},

abstract = {In this article, we consider the classical Jacobi theta functions$\theta_i(z)$, $i=1,2,3,4$ and show that the ideal of all polynomialrelations among them with coefficients in$K :=\setQ(\theta_2(0|\tau),\theta_3(0|\tau),\theta_4(0|\tau))$ isgenerated by just two polynomials, that correspond to well knownidentities among Jacobi theta functions.},

series = {Texts & Monographs in Symbolic Computation},

number = {18-09},

pages = {259--268},

publisher = {Springer International Publishing},

address = {Cham},

isbn_issn = {978-3-030-04479-4},

year = {2019},

note = {Also available as RISC Report 18-09 http://www.risc.jku.at/publications/download/risc_5719/thetarelations.pdf},

editor = {Johannes Blümlein and Carsten Schneider and Peter Paule},

refereed = {yes},

length = {9},

url = {https://doi.org/10.1007/978-3-030-04480-0_11}

}

[Ye]

@**article**{RISC5286,

author = {Liangjie Ye},

title = {{Elliptic Function Based Algorithms to Prove Jacobi Theta Function Relations}},

language = {english},

journal = {Journal of Symbolic Computation, to appear},

pages = {1--25},

isbn_issn = {-},

year = {2017},

refereed = {yes},

length = {25}

}

author = {Liangjie Ye},

title = {{Elliptic Function Based Algorithms to Prove Jacobi Theta Function Relations}},

language = {english},

journal = {Journal of Symbolic Computation, to appear},

pages = {1--25},

isbn_issn = {-},

year = {2017},

refereed = {yes},

length = {25}

}

[Ye]

@**article**{RISC5455,

author = {Liangjie Ye},

title = {{A Symbolic Decision Procedure for Relations Arising among Taylor Coefficients of Classical Jacobi Theta Functions}},

language = {english},

journal = {Journal of Symbolic Computation },

volume = {82},

pages = {134--163},

isbn_issn = {ISSN: 0747-7171},

year = {2017},

refereed = {yes},

length = {30}

}

author = {Liangjie Ye},

title = {{A Symbolic Decision Procedure for Relations Arising among Taylor Coefficients of Classical Jacobi Theta Functions}},

language = {english},

journal = {Journal of Symbolic Computation },

volume = {82},

pages = {134--163},

isbn_issn = {ISSN: 0747-7171},

year = {2017},

refereed = {yes},

length = {30}

}

[Ye]

@**phdthesis**{RISC5463,

author = {Liangjie Ye},

title = {{Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities}},

language = {english},

year = {2017},

note = {Updated version in June 2017},

translation = {0},

school = {RISC and the DK program Linz},

length = {122}

}

author = {Liangjie Ye},

title = {{Complex Analysis Based Computer Algebra Algorithms for Proving Jacobi Theta Function Identities}},

language = {english},

year = {2017},

note = {Updated version in June 2017},

translation = {0},

school = {RISC and the DK program Linz},

length = {122}

}

[Ye]

@**article**{RISC4569,

author = {Qunying Liao and Liangjie Ye},

title = {{Lower Bounds and Constructions for q-ary Codes Correcting Asymmetric Errors}},

language = {english},

journal = {Advances in Mathematics(China)},

volume = {42},

number = {6},

pages = {795--800},

isbn_issn = {ISSN:1000-0917 },

year = {2011},

refereed = {yes},

length = {6},

url = {http://advmath.pku.edu.cn/EN/volumn/volumn_1337.shtml}

}

author = {Qunying Liao and Liangjie Ye},

title = {{Lower Bounds and Constructions for q-ary Codes Correcting Asymmetric Errors}},

language = {english},

journal = {Advances in Mathematics(China)},

volume = {42},

number = {6},

pages = {795--800},

isbn_issn = {ISSN:1000-0917 },

year = {2011},

refereed = {yes},

length = {6},

url = {http://advmath.pku.edu.cn/EN/volumn/volumn_1337.shtml}

}

Phone: +43 732 2468 9921

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