RISC JKU

Cristian-Silviu Radu, Dr.

RISC Faculty

Publications

Koustav Banerjee, Peter Paule, Cristian-Silviu Radu, Carsten Schneider. Error bounds for the asymptotic expansion of the partition function. Rocky Mt J Math to appear, pp. ?-?. 2023. ISSN: 357596. arXiv:2209.07887 [math.NT]. [url] [bib]
K. Banerjee, P. Paule, C. S. Radu, W. H. Zeng. New inequalities for p(n) and log p(n). Research Institute for Symbolic Computation, JKU, Linz. Technical report no. RISC6607, 2022. To appear in the Ramanujan Journal. [pdf] [bib]
Nicolas Allen Smoot, Cristian-Silviu Radu. A method of verifying partition congruences by symbolic computation. Journal of Symbolic Computation 104, pp. 105-133. 2021. 0747-7171. [url] [pdf] [bib]
Peter Paule, Cristian-Silviu Radu. Holonomic relations for modular functions and forms: First guess, then prove. International Journal of Number Theory 17(3), pp. 713-759. 2021. World Scientific, 1793-0421. [url] [bib]
Ralf Hemmecke, Peter Paule, Silviu Radu. Construction of modular function bases for $Gamma_0(121)$ related to $p(11n+6)$. Integral Transforms and Special Functions 32(5-8), pp. 512-527. 2021. Taylor & Francis, 1065-2469. [url] [bib]
Peter Paule, Cristian-Silviu Radu. An algorithm to prove holonomic differential equations for modular forms. In: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019., Bostan A., Raschel K. (ed.), Springer Proceedings in Mathematics & Statistics 373, pp. 367-420. 2021. Springer, Cham, 978-3-030-84303-8. [url] [bib]
Mark van Hoeij and Cristian-Silviu Radu . Computing an order complete basis for M∞(N) and applications. In: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019, Bostan A., Raschel K. (ed.), Springer Proceedings in Mathematics & Statistics 373, pp. 355-366. 2021. Springer, Cham, 978-3-030-84303-8. [url] [bib]
Christian Krattenthaler, Mircea Merca, Cristian-Silviu Radu. Infinite product formulae for generating functions for sequences of squares. In: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2019, Bostan A., Raschel K. (ed.), Springer Proceedings in Mathematics & Statistics 373, pp. 193-236. 2021. Springer, Cham, 978-3-030-84303-8. [url] [bib]
Peter Paule, Cristian-Silviu Radu. An algorithm to prove holonomic differential equations for modular forms. Technical report no. 20-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. May 2020. A final version appeared in: Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS 2029, eds.: A. Bostan and K. Raschel, Springer, 2021. [pdf] [bib]
Radu, Cristian-Silviu. A reduction theorem of certain relations modulo p involving modular forms. In: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra, in Honour of Peter Paule on his 60th Birthday, V. Pillwein, C. Schneider (ed.), pp. 317-337. 2020. Springer, 978-3-030-44558-4. [url] [pdf] [bib]
Peter Paule, Silviu Radu. Holonomic Relations for Modular Functions and Forms: First Guess, then Prove. RISC. Technical report no. 20-14, 2020. [bib]
Ralf Hemmecke, Silviu Radu. Construction of all Polynomial Relations among Dedekind Eta Functions of Level $N$. Journal of Symbolic Compuation 95, pp. 39-52. 2019. ISSN 0747-7171. Also available as RISC Report 18-03 http://www.risc.jku.at/publications/download/risc_5561/etarelations.pdf. [url] [bib]
Ralf Hemmecke, Silviu Radu, Liangjie Ye. The Generators of all Polynomial Relations among Jacobi Theta Functions. 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. [url] [bib]
Peter Paule, Silviu Radu. A UNIFIED ALGORITHMIC FRAMEWORK FOR RAMANUJAN'S CONGRUENCES MODULO POWERS OF 5, 7, AND 11. Technical report no. 19-09 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. submitted, 2019. [pdf] [bib]
Peter Paule, Silviu Radu. A proof of the Weierstrass gap theorem not using the Riemann-Roch formula. Annals of Combinatorics 23(19-02), pp. 963-1007. May 2019. Springer, 0218-0006. [url] [bib]
Cristian-Silviu Radu. An algorithm to prove algebraic relations involving eta quotients. Annals of Combinatorics 22, pp. 377-391. 2018. Springer, 0219-3094. [url] [pdf] [bib]
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. Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations. 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. 2018. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [url] [bib]
J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C.G. Raab, C.-S. Radu, C. Schneider. Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams. J. Math. Phys. 59(062305), pp. 1-55. 2018. ISSN 0022-2488. arXiv:1706.01299 [hep-th]. [url] [pdf] [bib]
Peter Paule, Cristian-Silviu Radu. Rogers-Ramanujan functions, modular functions, and computer algebra. In: Advances in Computer Algebra - In Honour of Sergei Abramov's 70th Birthday, C. Schneider, E. Zima. (ed.), Springer Proceedings in Mathematics & Statistics 226, pp. 229-280. 2018. Springer, Cham, 978-3-319-73231-2. [url] [pdf] [bib]
Peter Paule, Cristian-Silviu Radu. A new witness identity for $11|p(11n+6)$. 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]
Christoph Koutschan and Martin Neumüller and Cristian-Silviu Radu. Inverse inequality estimates with symbolic computation. Advances in Applied Mathematics 80, pp. 1-23. 2016. 0196-8858. [url] [pdf] [bib]
Peter Paule, Silviu Radu. Partition analysis, modular functions, and computer algebra. In: Recent Trends in Combinatorics, IMA Volume, A. Beveridge, J. R. Griggs, L. Hogben, G. Musiker, P. Tetali (ed.), The IMA Volumes in Mathematics and its Applications 159, pp. 511-543. 2016. Springer, Cham, 978-3-319-24296-5. [url] [pdf] [bib]
Cristian-Silviu Radu. A note on a problem proposed by Kim and Lisonek. In: Computer Algebra and Polynomials, J. Gutierrez, J. Schicho, M. Weimann (ed.), Lecture notes in Computer Science 8942, pp. 151-156. 2015. Springer, Cham, 978-3-319-15080-2. [url] [bib]
CRISTIAN-SILVIU RADU. An algorithmic approach to Ramanujan-Kolberg identities. Journal of Symbolic Computation 68(1), pp. 225-253. 2015. 0747-7171. [url] [pdf] [bib]
Peter Paule, Silviu Radu. Partition Analysis, Modular Functions, and Computer Algebra. Technical report no. 15-14 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. In Recent Trends in Combinatorics, IMA Volume 511-543, 2015. [pdf] [bib]
Cristian-Silviu Radu. Proof of a conjecture by Ahlgren and Ono on the non-existence of certain partition congruences. Transactions of the American Mathematical Society 365, pp. 4881-4894. 2013. 1088-6850(e), 0002-9947(p) . [url] [pdf] [bib]
Cristian-Silviu Rand, James Sellers. An extensive analysis of the parity of broken 3-diamond partitions. Journal of Number Theory 133(11), pp. 3703-3716. 2013. 0022-314X. [url] [pdf] [bib]
CRISTIAN-SILVIU RADU, JAMES SELLERS. Congruences modulo squares of primes for Fu's k dots bracelet partitions. International Journal of Number Theory 9(4), pp. 939-943. 2013. World Scientific, 1793-0421. [url] [pdf] [bib]
CRISTIAN-SILVIU RADU, JAMES SELLERS. Infinitely many congruences for broken 2-diamond partitions modulo 3. Journal of Combinatorics and Number Theory 4(3), pp. 195-200. 2013. Nova Science Publishers, 1942-5600. [pdf] [bib]
Cristian-Silviu Radu. A proof of Subbarao's conjecture. Journal fuer Reine und angewandte Mathematik 2012(672), pp. 161-175. 2012. De Gruyter, 1435-5345. [url] [pdf] [bib]
Peter Paule, Cristian-Silviu Radu. The Andrews-Sellers family of partition congruences. Advances in Mathematics 230(3), pp. 819-838. 2012. 0001-8708. [url] [pdf] [bib]
Silviu Radu, James Sellers. Congruences Modulo Squares of Primes for Fu's Dots Bracelet Partitions. Technical report no. 12-13 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. 2012. [pdf] [bib]
Silviu Radu, James Sellers. Parity results for broken k-diamond partitions and (2k+1)-cores. Acta Arithmetica, pp. 43-52. 2011. ISSN 0065-1036. [bib]
Silviu Radu, James Sellers. Congruence Properties Modulo 5 and 7 for the pod Function. International Journal of Number Theory 8, pp. 2249-2259. 2011. 1793-7310. [bib]
Silviu Radu. An algorithmic approach to Ramanujan's congruences and related problems. RISC Linz. PhD Thesis. 2010. [bib]
Peter Paule, Silviu Radu. Infinite families of strange partition congruences for broken 2-diamonds . The Ramanujan Journal 23, pp. 409-416. 2010. 1382-4090. [url] [pdf] [bib]
Cristian-Silviu Radu. An Algorithmic Approach to Ramanujan’s Congruences and Related Problems. RISC-JKU. PhD Thesis. 2010. [pdf] [bib]
Peter Paule, Silviu Radu. A Proof of Sellers' Conjecture. RISC. Technical report no. 09-17, 2009. [pdf] [bib]
Silviu Radu. An algorithmic approach to Ramanujan congruences . Ramanujan Journal 20(2), pp. 215-251. 2009. 1382-4090 . [url] [pdf] [bib]
Silviu Radu. New Upper Bounds on Rubik's cube. Combinatorics. Technical report no. 07-08, 2007. [bib]


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