[Paule]
Holonomic Relations for Modular Functions and Forms: First Guess, then Prove
Peter Paule, Silviu Radu
2020. [pdf]
[bib]
@techreport{RISC6081,
author = {Peter Paule and Silviu Radu},
title = {{Holonomic Relations for Modular Functions and Forms: First Guess, then Prove}},
language = {english},
year = {2020},
length = {46},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
Towards a symbolic summation theory for unspecified sequences
P. Paule, C. Schneider
In: Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, P. Paule, C. Schneider (ed.), Texts and Monographs in Symbolic Computation , pp. 351-390. 2019. Springer, ISBN 978-3-030-04479-4. arXiv:1809.06578 [cs.SC], doi.org/10.1007/978-3-030-04480-0_15. [url] [bib]
@incollection{RISC5750,
author = {P. Paule and C. Schneider},
title = {{Towards a symbolic summation theory for unspecified sequences}},
booktitle = {{Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
pages = {351--390},
publisher = {Springer},
isbn_issn = {ISBN 978-3-030-04479-4},
year = {2019},
note = {arXiv:1809.06578 [cs.SC], doi.org/10.1007/978-3-030-04480-0_15},
editor = {J. Blümlein and P. Paule and C. Schneider},
refereed = {yes},
length = {40},
url = {https://arxiv.org/abs/1809.06578}
}
[Paule]
A UNIFIED ALGORITHMIC FRAMEWORK FOR RAMANUJAN'S CONGRUENCES MODULO POWERS OF 5, 7, AND 11
Peter Paule, Silviu Radu
Technical report no. 19-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. submitted, 2019. [pdf]
[bib]
@techreport{RISC5979,
author = {Peter Paule and Silviu Radu},
title = {{A UNIFIED ALGORITHMIC FRAMEWORK FOR RAMANUJAN'S CONGRUENCES MODULO POWERS OF 5, 7, AND 11}},
language = {english},
number = {19-09},
year = {2019},
howpublished = {submitted},
length = {49},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
Construction of Modular Function Bases for $\Gamma_0(121)$ related to $p(11n+6)$
Ralh Hemmecke, Peter Paule, Silviu Radu
Technical report no. 19-10 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. October 2019. [url] [pdf]
[bib]
@techreport{RISC5983,
author = {Ralh Hemmecke and Peter Paule and Silviu Radu},
title = {{Construction of Modular Function Bases for $\Gamma_0(121)$ related to $p(11n+6)$}},
language = {english},
number = {19-10},
year = {2019},
month = {October},
keywords = {Ramanujan identities, bases for modular functions, integral bases},
sponsor = {FWF (SFB F50-06)},
length = {17},
url = {https://risc.jku.at/people/hemmecke/papers/integralbasis/},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
A Proof of the Weierstrass Gap Theorem not using the Riemann-Roch Formula
Peter Paule, Silviu Radu
Annals of Combinatorics 23(19-02), pp. 963-1007. May 2019. Springer, 0218-0006. [url] [bib]
@article{RISC6076,
author = {Peter Paule and Silviu Radu},
title = {{A Proof of the Weierstrass Gap Theorem not using the Riemann-Roch Formula}},
language = {english},
abstract = {https://doi.org/10.1007/s00026-019-00459-2},
journal = {Annals of Combinatorics},
volume = {23},
number = {19-02},
pages = {963--1007},
publisher = {Springer},
isbn_issn = {0218-0006},
year = {2019},
month = {May},
refereed = {no},
length = {47},
url = {https://link.springer.com/article/10.1007/s00026-019-00459-2}
}
[Paule]
Holonomic Tools for Basic Hypergeometric Functions
Christoph Koutschan, Peter Paule
In: Frontiers of Orthogonal Polynomials and q-Series, Xin Li, Zuhair Nashed (ed.), pp. ?-?. 2018. World Scientific Publishing, ISBN 978-981-3228-87-0. [pdf]
[bib]
@incollection{RISC5246,
author = {Christoph Koutschan and Peter Paule},
title = {{Holonomic Tools for Basic Hypergeometric Functions}},
booktitle = {{Frontiers of Orthogonal Polynomials and q-Series}},
language = {english},
pages = {?--?},
publisher = {World Scientific Publishing},
isbn_issn = {ISBN 978-981-3228-87-0},
year = {2018},
editor = {Xin Li and Zuhair Nashed},
refereed = {no},
length = {19}
}
[Paule]
A Unified Algorithmic Framework for Ramanujan's Congruences Modulo Powers of 5, 7, and 11
Peter Paule, Silviu Radu
2018. [pdf]
[bib]
@techreport{RISC5760,
author = {Peter Paule and Silviu Radu},
title = {{A Unified Algorithmic Framework for Ramanujan's Congruences Modulo Powers of 5, 7, and 11}},
language = {english},
year = {2018},
length = {49},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra
Peter Paule, Cristian-Silviu Radu
In: Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday, C. Schneider and E. Zima. (ed.), pp. 1-41. 2017. Springer, 1019-7168 . [pdf]
[bib]
@incollection{RISC5475,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{Rogers-Ramanujan Functions, Modular Functions, and Computer Algebra}},
booktitle = {{Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday}},
language = {english},
pages = {1--41},
publisher = {Springer},
isbn_issn = {1019-7168 },
year = {2017},
editor = {C. Schneider and E. Zima.},
refereed = {yes},
length = {41}
}
[Paule]
Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra
Manuel Kauers, Peter Paule, Greg Reid
ACM Communications in Computer Algebra 50(Issue 1), pp. 27-34. March 2016. 1932-2240. [pdf]
[bib]
@article{RISC5284,
author = {Manuel Kauers and Peter Paule and Greg Reid},
title = {{Workshop on Symbolic Combinatorics and Algorithmic Differential Algebra}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {Issue 1},
pages = {27--34},
isbn_issn = {1932-2240},
year = {2016},
month = {March},
refereed = {no},
length = {8}
}
[Paule]
A New Witness Identity for $11|p(11n+6)$
Peter Paule, Cristian-Silviu Radu
In: Analytic Number Theory, Modular Forms and q-Hypergeometric Series, George E. Andrews, Frank Garvan (ed.), pp. 625-640. 2016. Springer, 2194-1009. [pdf]
[bib]
@inproceedings{RISC5329,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{A New Witness Identity for $11|p(11n+6)$}},
booktitle = {{Analytic Number Theory, Modular Forms and q-Hypergeometric Series}},
language = {english},
pages = {625--640},
publisher = {Springer},
isbn_issn = { 2194-1009},
year = {2016},
editor = { George E. Andrews and Frank Garvan},
refereed = {yes},
length = {16}
}
[Paule]
Partition Analysis, Modular Functions, and Computer Algebra
Peter Paule, Silviu Radu
Technical report no. 15-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. In Recent Trends in Combinatorics, IMA Volume 511-543, 2015. [pdf]
[bib]
@techreport{RISC5167,
author = {Peter Paule and Silviu Radu},
title = {{Partition Analysis, Modular Functions, and Computer Algebra}},
language = {english},
number = {15-14},
year = {2015},
howpublished = {In Recent Trends in Combinatorics, IMA Volume 511-543},
length = {24},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
Partition Analysis, Modular Functions, and Computer Algebra
Peter Paule, Silviu Radu
In: Recent Trends in Combinatorics, IMA Volume, Andrew Beveridge, Jerrold R. Griggs, Leslie Hogben, Gregg Musiker, Prasad Tetali (ed.), pp. 511-543. 2015. Springer, 0940-6573. [pdf]
[bib]
@incollection{RISC5776,
author = {Peter Paule and Silviu Radu},
title = {{Partition Analysis, Modular Functions, and Computer Algebra}},
booktitle = {{Recent Trends in Combinatorics, IMA Volume}},
language = {english},
pages = {511--543},
publisher = {Springer},
isbn_issn = {0940-6573},
year = {2015},
editor = {Andrew Beveridge and Jerrold R. Griggs and Leslie Hogben and Gregg Musiker and Prasad Tetali},
refereed = {yes},
length = {33}
}
[Paule]
Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II
Christoph Koutschan, Peter Paule, Sergei K. Suslov
In: Algebraic and Algorithmic Aspects of Differential and Integral Operators, Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz (ed.), Lecture Notes in Computer Science 8372, pp. 135-145. 2014. Springer, Berlin Heidelberg, ISBN 978-3-642-54478-1. [pdf]
[bib]
@incollection{RISC4847,
author = {Christoph Koutschan and Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach II}},
booktitle = {{Algebraic and Algorithmic Aspects of Differential and Integral Operators}},
language = {english},
abstract = {We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic closure properties in a sophisticated way.},
series = {Lecture Notes in Computer Science},
volume = {8372},
pages = {135--145},
publisher = {Springer},
address = {Berlin Heidelberg},
isbn_issn = {ISBN 978-3-642-54478-1},
year = {2014},
editor = {Moulay Barkatou and Thomas Cluzeau and Georg Regensburger and Markus Rosenkranz},
refereed = {yes},
length = {11}
}
[Paule]
Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.
Peter Paule, Sergei K. Suslov
In: Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013, Carsten Schneider, Johannes Blümlein (ed.), pp. 225-241. 2013. Springer, 978-3-7091-1615-9. [bib]
@incollection{RISC4718,
author = {Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I.}},
booktitle = {{Computer Algebra in Quantum Field Theory, Texts and Monographs in Symbolic Computation, Springer, 2013}},
language = {english},
pages = {225--241},
publisher = {Springer},
isbn_issn = {978-3-7091-1615-9},
year = {2013},
editor = {Carsten Schneider and Johannes Blümlein},
refereed = {no},
length = {17}
}
[Paule]
Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order
S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann
In: Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions, C. Schneider, J. Bluemlein (ed.), Texts and Monographs in Symbolic Computation , pp. 75-96. 2013. Springer, ISBN-13: 978-3709116159. arXiv:1305.4818 [cs.SC], doi.org/10.1007/978-3-7091-1616-6_3. [url] [bib]
@incollection{RISC4721,
author = {S. Gerhold and M. Kauers and C. Koutschan and P. Paule and C. Schneider and B. Zimmermann},
title = {{Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order}},
booktitle = {{Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
pages = {75--96},
publisher = {Springer},
isbn_issn = {ISBN-13: 978-3709116159},
year = {2013},
note = {arXiv:1305.4818 [cs.SC], doi.org/10.1007/978-3-7091-1616-6_3},
editor = {C. Schneider and J. Bluemlein},
refereed = {no},
length = {22},
url = {http://arxiv.org/abs/1305.4818}
}
[Paule]
Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift
Peter Paule
1st edition, 2013. Springer, 978-3-319-00965-0. [bib]
@booklet{RISC4850,
author = {Peter Paule},
title = {{Mathematics, Computer Science and Logic - A Never Ending Story The Bruno Buchberger Festschrift}},
language = {english},
publisher = {Springer},
isbn_issn = {978-3-319-00965-0},
year = {2013},
edition = {1st},
translation = {0},
length = {113}
}
[Paule]
The Andrews-Sellers Family of Partition Congruences
Peter Paule, Cristian-Silviu Radu
Advances in Mathematics, pp. 819-838. 2012. 0001-8708. [pdf]
[bib]
@article{RISC4550,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{The Andrews-Sellers Family of Partition Congruences}},
language = {english},
journal = {Advances in Mathematics},
pages = {819--838},
isbn_issn = {0001-8708},
year = {2012},
refereed = {yes},
length = {20}
}
[Paule]
Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I
Peter Paule, Sergei K. Suslov
Technical report no. 12-12 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 2012. Published in: Computer Algebra in Quantum Field Theory Integration, Summation and Special Functions, Buchreihe: Texts & Monographs in Symbolic Computation, Verlag: Springer Vienna, Print ISBN: 978-3-7091-1615-9.. [pdf]
[bib]
@techreport{RISC4603,
author = {Peter Paule and Sergei K. Suslov},
title = {{Relativistic Coulomb Integrals and Zeilbergers Holonomic Systems Approach. I}},
language = {english},
number = {12-12},
year = {2012},
note = {Published in: Computer Algebra in Quantum Field Theory Integration, Summation and Special Functions, Buchreihe: Texts & Monographs in Symbolic Computation, Verlag: Springer Vienna, Print ISBN: 978-3-7091-1615-9.},
length = {16},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
MacMahon's Dream
George E. Andrews and Peter Paule
In: Partitions, q-Series, and Modular Forms, K. Alladi and F. Garvan (ed.), Developments in Mathematics 23, pp. 1-12. 2012. Springer, 978-1-4614-0028-8. [bib]
@incollection{RISC5157,
author = {George E. Andrews and Peter Paule},
title = {{MacMahon's Dream}},
booktitle = {{Partitions, q-Series, and Modular Forms}},
language = {english},
series = {Developments in Mathematics},
volume = {23},
pages = {1--12},
publisher = {Springer},
isbn_issn = {978-1-4614-0028-8},
year = {2012},
editor = {K. Alladi and F. Garvan},
refereed = {yes},
length = {12}
}
[Paule]
The Concrete Tetrahedron
Manuel Kauers, Peter Paule
Text and Monographs in Symbolic Computation 1st edition, 2011. Springer Wien, 978-3-7091-0444-6. [bib]
@book{RISC4162,
author = {Manuel Kauers and Peter Paule},
title = {{The Concrete Tetrahedron}},
language = {english},
series = {Text and Monographs in Symbolic Computation},
publisher = {Springer Wien},
isbn_issn = {978-3-7091-0444-6},
year = {2011},
edition = {1st},
translation = {0},
length = {210}
}
