RISC PhD Fellowships 2017

@article{RISC7068,
author = {P. Paule and C. Schneider},
title = {{Creative Telescoping for Hypergeometric Double Sums}},
language = {english},
abstract = {We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute rational solutions of parameterized linear recurrences.},
journal = {J. Symb. Comput.},
volume = {128},
number = {102394},
pages = {1--30},
isbn_issn = {ISSN: 0747-7171},
year = {2025},
note = {Symbolic Computation and Combinatorics: A special issue in memory and honor of Marko Petkovšek, edited by Shaoshi Chen, Sergei Abramov, Manuel Kauers, Eugene Zima},
refereed = {yes},
keywords = {creative telescoping; symbolic summation, hypergeometric multi-sums, contiguous relations, parameterized recurrences, rational solutions},
length = {30},
url = {https://doi.org/10.1016/j.jsc.2024.102394}
}

@article{RISC6755,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The first--order factorizable contributions to the three--loop massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},
language = {english},
abstract = {The unpolarized and polarized massive operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$contain first--order factorizable and non--first--order factorizable contributions in the determining difference or differential equations of their master integrals. We compute their first--order factorizable contributions in the single heavy mass case for all contributing Feynman diagrams. Moreover, we present the complete color--$zeta$ factors for the cases in which also non--first--order factorizable contributions emerge in the master integrals, but cancel in the final result as found by using the method of arbitrary high Mellin moments. Individual contributions depend also on generalized harmonic sums and on nested finite binomial and inverse binomial sums in Mellin $N$--space, and correspondingly, on Kummer--Poincar'e and square--root valued alphabets in Bjorken--$x$ space. We present a complete discussion of the possibilities of solving the present problem in $N$--space analytically and we also discuss the limitations in the present case to analytically continue the given $N$--space expressions to $N in mathbb{C}$ by strict methods. The representation through generating functions allows a well synchronized representation of the first--order factorizable results over a 17--letter alphabet. We finally obtain representations in terms of iterated integrals over the corresponding alphabet in $x$--space, also containing up to weight {sf w = 5} special constants, which can be rationalized to Kummer--Poincar'e iterated integrals at special arguments. The analytic $x$--space representation requires separate analyses for the intervals $x in [0,1/4], [1/4,1/2], [1/2,1]$ and $x > 1$. We also derive the small and large $x$ limits of the first--order factorizable contributions. Furthermore, we perform comparisons to a number of known Mellin moments, calculated by a different method for the corresponding subset of Feynman diagrams, and an independent high--precision numerical solution of the problems.},
journal = {Nuclear Physics B},
volume = {999},
number = {116427},
pages = {1--42},
isbn_issn = {ISSN 0550-3213},
year = {2024},
note = {arXiv:2311.00644 [hep-ph]},
refereed = {yes},
keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, nested integrals, nested sums},
length = {42},
url = {https://doi.org/10.1016/j.nuclphysb.2023.116427}
}

@article{RISC7058,
author = {J. Ablinger and A. Behring and J. Bluemlein and A. De Freitas and A. von Manteuffel and C. Schneider and K. Schoenwald},
title = {{The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$}},
language = {english},
abstract = {The non-first-order-factorizable contributions to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $Delta A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method basedon series expansions and utilize the first-order differential equations for the master integrals whichdoes not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(ep^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x in ]0,infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.},
journal = {Physics Letter B},
volume = {854},
number = {138713},
pages = {1--8},
isbn_issn = {ISSN 0370-2693},
year = {2024},
note = {arXiv:2403.00513 [[hep-ph]},
refereed = {yes},
keywords = {Feynman diagram, massive operator matrix elements, computer algebra, differential equations, difference equations, coupled systems, numerics},
length = {8},
url = {https://doi.org/10.1016/j.physletb.2024.138713}
}

@article{RISC7060,
author = {Z. Chen and Z. Chen and J. Obrovsky and A. Winterhof},
title = {{Maximum-order Complexity and 2-Adic Complexity}},
language = {english},
abstract = {The 2-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results in the aperiodic case. In particular, the Nth 2-adic complexity has not been studied for any promising candidate of a pseudorandom sequence of finite length N. Also nothing seems be known for a part of the period of length N of any cryptographically interesting periodic sequence. Here we introduce the first method for this aperiodic case. More precisely, we study the relation between Nth maximum-order complexity and Nth 2-adic complexity of binary sequences and prove a lower bound on the Nth 2-adic complexity in terms of the Nth maximum-order complexity. Then any known lower bound on the Nth maximum-order complexity implies a lower bound on the Nth 2-adic complexity of the same order of magnitude. In the periodic case, one can prove a slightly better result. The latter bound is sharp, which is illustrated by the maximum-order complexity of ell -sequences. The idea of the proof helps us to characterize the maximum-order complexity of periodic sequences in terms of the unique rational number defined by the sequence. We also show that a periodic sequence of maximal maximum-order complexity must be also of maximal 2-adic complexity.},
journal = {IEEE Transactions on Information Theory},
volume = {70},
number = {8},
pages = { 6060--6067},
isbn_issn = {ISSN: 0018-9448},
year = {2024},
refereed = {yes},
keywords = {Complexity theory;Polynomials;Random sequences;Cryptography;Surveys;Shift registers;Mathematics;Pseudorandom sequences;maximum-order complexity;2-adic complexity;ℓ-sequences},
length = {8},
url = {https://doi.org/10.1109/TIT.2024.3405946}
}

@article{RISC6774,
author = {Jiayue Qi},
title = {{A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero}},
language = {english},
journal = {Journal of Symbolic Computation},
volume = {122},
number = {102253},
pages = {--},
isbn_issn = {ISSN: 0747-7171},
year = {2024},
refereed = {yes},
length = {52},
url = {https://doi.org/10.1016/j.jsc.2023.102253}
}

@article{RISC6688,
author = {E.D. Ocansey and C. Schneider},
title = {{Representation of hypergeometric products of higher nesting depths in difference rings}},
language = {english},
journal = {J. Symb. Comput.},
volume = {120},
pages = {1--50},
isbn_issn = {ISSN: 0747-7171},
year = {2024},
note = {arXiv:2011.08775 [cs.SC]},
refereed = {yes},
length = {50},
url = {https://doi.org/10.1016/j.jsc.2023.03.002}
}

@article{RISC6710,
author = {Koustav Banerjee and Peter Paule and Cristian-Silviu Radu and Carsten Schneider},
title = {{Error bounds for the asymptotic expansion of the partition function}},
language = {english},
abstract = {Asymptotic study on the partition function $p(n)$ began with the work of Hardy and Ramanujan. Later Rademacher obtained a convergent series for $p(n)$ and an error bound was given by Lehmer. Despite having this, a full asymptotic expansion for $p(n)$ with an explicit error bound is not known. Recently O'Sullivan studied the asymptotic expansion of $p^{k}(n)$-partitions into $k$th powers, initiated by Wright, and consequently obtained an asymptotic expansion for $p(n)$ along with a concise description of the coefficients involved in the expansion but without any estimation of the error term. Here we consider a detailed and comprehensive analysis on an estimation of the error term obtained by truncating the asymptotic expansion for $p(n)$ at any positive integer $n$. This gives rise to an infinite family of inequalities for $p(n)$ which finally answers to a question proposed by Chen. Our error term estimation predominantly relies on applications of algorithmic methods from symbolic summation. },
journal = {Rocky Mt J Math },
volume = {54},
number = {6},
pages = {1551--1592},
isbn_issn = {ISSN: 357596},
year = {2024},
note = {arXiv:2209.07887 [math.NT]},
refereed = {yes},
keywords = {partition function, asymptotic expansion, error bounds, symbolic summation},
length = {43},
url = {https://www.doi.org/10.1216/rmj.2024.54.1551}
}

@article{RISC6701,
author = {Koustav Banerjee},
title = {{Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach}},
language = {english},
journal = {Enumerative Combinatorics and Applications},
volume = {3},
pages = {1--4},
isbn_issn = {ISSN 2710-2335},
year = {2023},
refereed = {yes},
length = {5},
url = {https://doi.org/10.54550/ECA2023V3S2R12}
}

@article{RISC6700,
author = {K. Banerjee},
title = {{Inequalities for the modified Bessel function of first kind of non-negative order}},
language = {english},
journal = {Journal of Mathematical Analysis and Applications},
volume = {524},
pages = {1--28},
publisher = {Elsevier},
isbn_issn = {ISSN 1096-0813},
year = {2023},
refereed = {yes},
length = {28},
url = {https://doi.org/10.1016/j.jmaa.2023.127082}
}