Symbolische Summation in Differenzkörpern (Symbolic Summation in Difference Fields)

Project Description

P.Paule.
Budget: 144.018,–

Project Lead

Project Duration

01/12/2003 - 31/01/2007

Publications

2017

Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses

J. Ablinger, J. Blümlein, A. De Freitas, A. Hasselhuhn, C. Schneider, F. Wißbrock

Nucl. Phys. B. 921, pp. 585-688. 2017. ISSN 0550-3213. arXiv:1705.07030 [hep-ph]. [url]
[bib]
@article{RISC5451,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Hasselhuhn and C. Schneider and F. Wißbrock},
title = {{Three Loop Massive Operator Matrix Elements and Asymptotic Wilson Coefficients with Two Different Masses}},
language = {english},
journal = {Nucl. Phys. B.},
volume = {921},
pages = {585--688},
isbn_issn = {ISSN 0550-3213},
year = {2017},
note = {arXiv:1705.07030 [hep-ph]},
refereed = {yes},
length = {99},
url = {https://arxiv.org/abs/1705.07030}
}

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}
}

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C.G. Raab, C.-S. Radu, C. Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-13. 2017. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [url]
[bib]
@inproceedings{RISC5350,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},
title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 069},
pages = {1--13},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = {arXiv:1711.09742 [hep-ph]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {13},
url = {https://pos.sissa.it/290/069/pdf}
}

Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects

C. Schneider

J. Symb. Comput. 80(3), pp. 616-664. 2017. ISSN 0747-7171. arXiv:1603.04285 [cs.SC]. [url]
[bib]
@article{RISC5270,
author = {C. Schneider},
title = {{Summation Theory II: Characterizations of $R\Pi\Sigma$-extensions and algorithmic aspects}},
language = {english},
journal = {J. Symb. Comput.},
volume = {80},
number = {3},
pages = {616--664},
isbn_issn = {ISSN 0747-7171},
year = {2017},
note = {arXiv:1603.04285 [cs.SC]},
refereed = {yes},
length = {54},
url = {http://arxiv.org/abs/1603.04285}
}

Asymptotic and exact results on the complexity of the Novelli-Pak-Stoyanovskii algorithm

C. Schneider, R. Sulzgruber

Electron. J. Combin. 24(2), pp. 1-33. 2017. ISSN: 1077-8926. #P2.28, arXiv:1606.07597. [url]
[bib]
@article{RISC5318,
author = {C. Schneider and R. Sulzgruber},
title = {{Asymptotic and exact results on the complexity of the Novelli--Pak--Stoyanovskii algorithm}},
language = {english},
journal = {Electron. J. Combin. },
volume = {24},
number = {2},
pages = {1--33},
isbn_issn = {ISSN: 1077-8926},
year = {2017},
note = {#P2.28, arXiv:1606.07597},
refereed = {yes},
length = {25},
url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p28}
}

The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory

J. Blümlein, C. Schneider

Physics Letters B 771, pp. 31-36. 2017. ISSN 0370-2693. arXiv:1701.04614 [hep-ph]. [url]
[bib]
@article{RISC5402,
author = {J. Blümlein and C. Schneider},
title = {{The Method of Arbitrarily Large Moments to Calculate Single Scale Processes in Quantum Field Theory}},
language = {english},
journal = {Physics Letters B},
volume = {771},
pages = {31--36},
isbn_issn = {ISSN 0370-2693},
year = {2017},
note = {arXiv:1701.04614 [hep-ph]},
refereed = {yes},
length = {6},
url = {https://doi.org/10.1016/j.physletb.2017.05.001}
}

The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2, \rm N_F)}$

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider

Nucl. Phys. B. 922, pp. 1-40. 2017. ISSN 0550-3213.. arXiv:1705.01508 [hep-ph]. [url]
[bib]
@article{RISC5449,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},
title = {{The Three-Loop Splitting Functions $P_{qg}^{(2)}$ and $P_{gg}^{(2,\rm N_F)}$}},
language = {english},
journal = {Nucl. Phys. B.},
volume = {922},
pages = {1--40},
isbn_issn = {ISSN 0550-3213.},
year = {2017},
note = {arXiv:1705.01508 [hep-ph]},
refereed = {yes},
length = {40},
url = {https://arxiv.org/abs/1705.01508}
}

Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider

In: Proceedings of QCDEV2017, L. Gamberg, A. Prokudin, J.W. Qiu and A. Radyushkin (ed.)PoS(QCDEV2017)031 , pp. 1-10. 2017. ISSN 1824-8039. arXiv:1711.07957 [hep-ph]. [url]
[bib]
@inproceedings{RISC5506,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},
title = {{Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering: Recent Results}},
booktitle = {{Proceedings of QCDEV2017}},
language = {english},
volume = {PoS(QCDEV2017)031 },
pages = {1--10},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = {arXiv:1711.07957 [hep-ph]},
editor = {L. Gamberg and A. Prokudin and J.W. Qiu and A. Radyushkin},
refereed = {no},
length = {10},
url = {https://pos.sissa.it/308/}
}

The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme

J. Ablinger, J. Blümlein, A. De Freitas, A. Goedicke, C. Schneider, K. Schönwald, F. Wißbrock

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 071, pp. 1-20. 2017. ISSN 1824-8039. arXiv:1712.00745 [hep-ph]. [url]
[bib]
@inproceedings{RISC5513,
author = {J. Ablinger and J. Blümlein and A. De Freitas and A. Goedicke and C. Schneider and K. Schönwald and F. Wißbrock},
title = {{The massive 3-loop operator matrix elements with two masses and the generalized variable flavor number scheme}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 071},
pages = {1--20},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = { arXiv:1712.00745 [hep-ph]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {20},
url = {https://pos.sissa.it/290/071/pdf}
}

Special functions, transcendentals and their numerics

Jakob Ablinger, Johannes Blümlein, Mark Round, Carsten Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 010, pp. 1-7. 2017. ISSN 1824-8039. arXiv:1712.08541 [hep-th]. [url]
[bib]
@inproceedings{RISC5521,
author = {Jakob Ablinger and Johannes Blümlein and Mark Round and Carsten Schneider},
title = {{Special functions, transcendentals and their numerics}},
booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},
language = {english},
volume = {PoS (RADCOR2017) 010},
pages = {1--7},
isbn_issn = {ISSN 1824-8039},
year = {2017},
note = { arXiv:1712.08541 [hep-th]},
editor = {A. Hoang and C. Schneider},
refereed = {no},
length = {7},
url = {https://pos.sissa.it/290/010/pdf}
}

Heavy quark form factors at two loops in perturbative QCD

J. Ablinger, A. Behring, J. Blümlein, G. Falcioni, A. De Freitas, P. Marquard, N. Rana, C. Schneider

ACTA PHYSICA POLONICA B 48(12), pp. 2155-2166. 2017. ISSN 0587-4254. Presented at the XLI International Conference of Theoretical Physics “Matter to the Deepest”, Podlesice, Poland, September 3–8, 2017, arXiv:1711.04880 [hep-ph]. [url]
[bib]
@article{RISC5539,
author = {J. Ablinger and A. Behring and J. Blümlein and G. Falcioni and A. De Freitas and P. Marquard and N. Rana and C. Schneider},
title = {{Heavy quark form factors at two loops in perturbative QCD}},
language = {english},
journal = {ACTA PHYSICA POLONICA B},
volume = {48},
number = {12},
pages = {2155--2166},
isbn_issn = { ISSN 0587-4254},
year = {2017},
note = {Presented at the XLI International Conference of Theoretical Physics “Matter to the Deepest”, Podlesice, Poland, September 3–8, 2017, arXiv:1711.04880 [hep-ph]},
refereed = {yes},
length = {12},
url = {http://www.actaphys.uj.edu.pl/findarticle?series=Reg&vol=48&page=2155}
}

2016

Heavy flavour corrections to polarised and unpolarised deep-inelastic scattering at 3-loop order

Jakob Ablinger, Arnd Behring, Johannes Blümlein, Abilio De Freitas, Alexander Hasselhuhn, Andreas von Manteuffel, Mark Round, Carsten Schneider, Fabian Wißbrock

In: Proceedings of the QCD Evolution 2016, PoS(QCDEV2016)052, pp. 1-16. 2016. National Institute for Subatomic Physics (Nikhef) in Amsterdam, ISSN 1824-8039. arXiv:1611.01104 [hep-ph]. [url]
[bib]
@inproceedings{RISC5386,
author = {Jakob Ablinger and Arnd Behring and Johannes Blümlein and Abilio De Freitas and Alexander Hasselhuhn and Andreas von Manteuffel and Mark Round and Carsten Schneider and Fabian Wißbrock},
title = {{Heavy flavour corrections to polarised and unpolarised deep-inelastic scattering at 3-loop order}},
booktitle = {{Proceedings of the QCD Evolution 2016}},
language = {english},
volume = {PoS(QCDEV2016)052},
pages = {1--16},
isbn_issn = {ISSN 1824-8039},
year = {2016},
note = {arXiv:1611.01104 [hep-ph]},
editor = {?},
refereed = {yes},
organization = {National Institute for Subatomic Physics (Nikhef) in Amsterdam},
length = {16},
url = {https://arxiv.org/abs/1611.01104}
}

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}
}

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}
}

A Difference Ring Theory for Symbolic Summation

C. Schneider

J. Symb. Comput. 72, pp. 82-127. 2016. ISSN 0747-7171. arXiv:1408.2776 [cs.SC]. [url]
[bib]
@article{RISC5125,
author = {C. Schneider},
title = {{A Difference Ring Theory for Symbolic Summation}},
language = {english},
journal = {J. Symb. Comput.},
volume = {72},
pages = {82--127},
isbn_issn = {ISSN 0747-7171},
year = {2016},
note = { arXiv:1408.2776 [cs.SC]},
refereed = {yes},
length = {46},
url = {http://dx.doi.org/10.1016/j.jsc.2015.02.002}
}

Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra

J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, A. von Manteuffel, C. Schneider

Comput. Phys. Comm. 202, pp. 33-112. 2016. ISSN 0010-4655. arXiv:1509.08324 [hep-ph]. [url]
[bib]
@article{RISC5173,
author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and A. von Manteuffel and C. Schneider},
title = {{Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra}},
language = {english},
journal = {Comput. Phys. Comm.},
volume = {202},
pages = {33--112},
isbn_issn = {ISSN 0010-4655},
year = {2016},
note = {arXiv:1509.08324 [hep-ph]},
refereed = {yes},
length = {80},
url = {http://arxiv.org/abs/1509.08324}
}

Symbolic Summation in Difference Rings and Applications

C. Schneider

In: Proc. ISSAC 2016, M. Rosenkranz (ed.), pp. 9-12. 2016. ISBN 978-1-4503-4380-0/16/07. [pdf]
[bib]
@inproceedings{RISC5287,
author = {C. Schneider},
title = {{Symbolic Summation in Difference Rings and Applications}},
booktitle = {{Proc. ISSAC 2016}},
language = {english},
pages = {9--12},
isbn_issn = {ISBN 978-1-4503-4380-0/16/07},
year = {2016},
editor = {M. Rosenkranz},
refereed = {no},
length = {4}
}

Representation of hypergeometric products in difference rings

E.D. Ocansey, C. Schneider

ACM Communications in Computer Algebra 50(4), pp. 161-163. 2016. ISSN 1932-2240 . Extended abstract of the poster presentation at ISSAC 2016. [pdf]
[bib]
@article{RISC5316,
author = {E.D. Ocansey and C. Schneider},
title = {{Representation of hypergeometric products in difference rings}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {4},
pages = {161--163},
isbn_issn = {ISSN 1932-2240 },
year = {2016},
note = {Extended abstract of the poster presentation at ISSAC 2016},
refereed = {yes},
length = {3}
}

Denominator Bounds for Higher Order Systems of Linear Recurrence Equations

J. Middeke, C. Schneider

ACM Communications in Computer Algebra 50(4), pp. 185-187. 2016. ISSN 1932-2240. Extended abstract of the poster presentation at ISSAC 2016. [pdf] [pdf]
[bib]
@article{RISC5317,
author = {J. Middeke and C. Schneider},
title = {{Denominator Bounds for Higher Order Systems of Linear Recurrence Equations}},
language = {english},
journal = {ACM Communications in Computer Algebra},
volume = {50},
number = {4},
pages = {185--187},
isbn_issn = {ISSN 1932-2240},
year = {2016},
note = {Extended abstract of the poster presentation at ISSAC 2016},
refereed = {no},
length = {2}
}

Evaluation of binomial double sums involving absolute values

C. Krattenthaler, C. Schneider

submitted, pp. 1-36. 2016. arXiv:1607.05314 [math.CO]. [url]
[bib]
@article{RISC5331,
author = {C. Krattenthaler and C. Schneider},
title = {{Evaluation of binomial double sums involving absolute values}},
language = {english},
journal = {submitted},
pages = {1--36},
isbn_issn = {?},
year = {2016},
note = {arXiv:1607.05314 [math.CO]},
refereed = {yes},
length = {36},
url = {https://arxiv.org/abs/1607.05314}
}

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