[Paule]
An Invitation to Analytic Combinatorics
Peter Paule (ed.), Stephen Melczer
Texts and Monographs in Symbolic Computation 1st edition, 2021. Springer, 978-3-030-67080-1. [bib]
@book{RISC6277,
author = {Peter Paule (ed.) and Stephen Melczer},
title = {{An Invitation to Analytic Combinatorics}},
language = {english},
series = {Texts and Monographs in Symbolic Computation},
publisher = {Springer},
isbn_issn = {978-3-030-67080-1},
year = {2021},
edition = {1st},
translation = {0},
length = {405}
}
[Paule]
Holonomic Relations for Modular Functions and Forms: First Guess, then Prove
Peter Paule, Silviu Radu
Technical report no. 20-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. 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},
number = {20-14},
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]
An algorithm to prove holonomic differential equations for modular forms
Peter Paule, Cristian-Silviu Radu
Technical report no. 20-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Schloss Hagenberg, 4232 Hagenberg, Austria. May 2020. [pdf] [bib]
@techreport{RISC6108,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{An algorithm to prove holonomic differential equations for modular forms}},
language = {english},
abstract = {Express a modular form $g$ of positive weight locally in terms of a modular function $h$ as$y(h)$, say. Then $y(h)$ as a function in $h$ satisfiesa holonomic differential equation; i.e., one which islinear with coefficients being polynomials in $h$.This fact traces back to Gau{\ss} and has beenpopularized prominently by Zagier. Using holonomicprocedures, computationally it is often straightforwardto derive such differential equations as conjectures.In the spirit of the ``first guess, then prove'' paradigm,we present a new algorithm to prove such conjectures.},
number = {20-05},
year = {2020},
month = {May},
keywords = {modular functions, modular forms, holonomic differential equations, holonomic functions and sequences, Fricke-Klein relations, $q$-series, partition congruences},
sponsor = {FWF SFB F50},
length = {48},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
}
[Paule]
An Introduction to Computational Origami
Peter Paule (ed.), Tetsuo Ida
Texts and Monographs of Symbolic Computation 1st edition, 2020. Springer, 978-3-319-59189-6. [bib]
@book{RISC6276,
author = {Peter Paule (ed.) and Tetsuo Ida},
title = {{An Introduction to Computational Origami}},
language = {english},
series = {Texts and Monographs of Symbolic Computation},
publisher = {Springer},
isbn_issn = {978-3-319-59189-6},
year = {2020},
edition = {1st},
translation = {0},
length = {201}
}
[Paule]
Holonomic relations for modular functions and forms: First guess, then prove
Peter Paule, Cristian-Silviu Radu
International Journal of Number Theory, pp. -. 2020. 0. [bib]
@article{RISC6279,
author = {Peter Paule and Cristian-Silviu Radu},
title = {{Holonomic relations for modular functions and forms: First guess, then prove}},
language = {english},
journal = {International Journal of Number Theory},
pages = {--},
isbn_issn = {0},
year = {2020},
refereed = {yes},
length = {46}
}
[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
Submitted to the RISC Report Series. 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}
}
