
Contact
Address:Doctoral Program Computational Mathematics Johannes Kepler University Altenberger Straße 69 A4040 Linz Austria
Publications
1. K. Banerjee and C. S. Radu. Optimality of error bounds for the asymptotic expansion of the modified Bessel function of first kind of nonnegative order, in preparation.
2. K. Banerjee and N. A. Smoot. kelongated plane partitions and powers of 7, in preparation.
3. K. Banerjee. Asymptotics for the cubic partition function and its applications, in preparation.
4. K. Banerjee. Divisibility of generalized 2colored partitions modulo powers of primes, in preparation.
5. K. Banerjee. Higher order Laguerre inequalities for the partition function and its consequences, in preparation.
6. K. Banerjee and M. G. Dastidar. Inequalities for the partition function arising from truncated theta series, submitted for publication (2022).
7. K. Banerjee. Invariants of quartic binary form and proofs of Chen's conjectures for partition function inequalities, submitted for publication (2022).
8. K. Banerjee. A unified framework to prove multiplicative inequalities for the partition function, submitted for publication (2022).
9. K. Banerjee and N. A. Smoot. The localization method applied to kelongated plane partitions and divisibility by 5, submitted for publication (2022).
10. K. Banerjee, P. Paule, C. Schneider, and C. S. Radu. Error bounds for the asymptotic expansion of the partition function, submitted for publication (2022).
11. K. Banerjee. Positivity of the second shifted difference of partitions and overpartitions: a combinatorial approach, submitted for publication (2022).
12. K. Banerjee and M. G. Dastidar. Hook type enumeration and parity of parts in partitions, submitted for publication (2022).
13. K. Banerjee and M. G. Dastidar. Revisiting the Jacobi triple product identity, submitted for publication (2022).
14. K. Banerjee. Inequalities for the modified Bessel function of first kind of nonnegative order, Journal of Mathematical Analysis and Applications (accepted for publication).
15. K. Banerjee and M. G. Dastidar. Ramanujan's theta functions and parity of parts and cranks of partitions, Annals of Combinatorics (2022).
16. K. Banerjee, P. Paule, C. S. Radu, and W. H. Zeng. New inequalities for p(n) and log p(n), Ramanujan Journal (2022).
17. K. Banerjee, S. Bhattacharjee, M. G. Dastidar, P. J. Mahanta, and M. P. Saikia. Parity biases in partitions and restricted partitions. European Journal of Combinatorics 103 (2022), p. 103522.
18. K. Banerjee, S. Bhattacharjee, M. G. Dastidar, P. J. Mahanta, and M. P. Saikia. Parity biases in partitions and restricted partitions (extended abstract), Seminaire Lotharingien de Combinatoire (Proceedings of FPSAC'22), 86B (2022).
19. K. Banerjee and M. G. Dastidar. Hook type tableaux and partition identities, Notes on Number Theory and Discrete Mathematics 28 (2022), pp. 635647.
20. K. Banerjee and A. Dixit. New representations for $\sigma(q)$ via reciprocity theorems, Analytic Number Theory, Modular Forms and qHypergeometric Series, Springer Proceedings in Mathematics and Statistics (2017), pp. 3957.
21. K. Banerjee and P. D. Adhikary. An elementary alternative proof for Chan's analogue of Ramanujan's most beautiful identity and some inequality of the cubic partition, Notes on Number Theory and Discrete Mathematics, 23 (2017), pp. 7787.
Short Curriculum Vitae
 Jan. 2019  Dec. 2022: Ph.D., Research Institute for Symbolic Computation, Johannes Kepler University, Austria. Advisor: Prof. Dr. Peter Paule, Coadvisor: Dr. Cristian Silviu Radu. Title of thesis: New asymptotics and inequalities related to the partition function.
 2014  2016 : M.Sc. in Mathematics, School of Mathematical Sciences, Ramakrishna Mission Vivekananda Educational and Research Institute (formerly known as: Ramakrishna Mission Vivekananda University), India.
 20112014: B.Sc. in Mathematics, Ramakrishna Mission Vidyamandira, University of Calcutta, India.
Research interests
Number Theory, Combinatorics, Special Functions.
Activities
Scientific Stays
 June, 2016  July, 2016 : Summer Research Internship Program, IIT Gandhinagar, Advisor: Assoc. Prof. Atul Dixit, topic: On certain restricted partition functions.
 July, 2017  Dec., 2017: Project Assistant, IISER, Tirupati, Host: Assoc. Prof. Anilatmaja Aryasomayajula, topic: AbelJacobi form.
Participation at colloquiums, workshops and conferences
 Aug. 08  10, 2016 : 29th International Conference of The Jangjeon Mathematical Society on Number theory and Special functions and it's applications, Pondicherry University, India.
 Jan. 29, 2019 : SFB Colloquium, RISC, Hagenberg, Austria.
 Feb. 25  March 01, 2019: Workshop and Winter School on Local Statistics of Point Sequences, JKU, Linz, Austria.
 March 19, 2019: DK Computational Mathematics Seminar, JKU (Title of talk  Arithmetics on Lattices).
 April 12, 2019: SFB Colloquium, University of Vienna, Austria.
 May 08, 2019: Algorithmic Combinatorics Seminar, RISC, JKU (Title of talk  Hook type and Partition Identities).
 June 06  09, 2019: Analytic and Combinatorial Number Theory:The Legacy of Ramanujan, in Honor of Prof. Bruce C. Berndt's 80th birthday, University of Illinois Urbana Champaign, Illinois, USA.
 June 12, 2019: SFB Colloquium, RICAM, Linz, Austria.
 June 24, 2019: RISC Forum, RISC, JKU (Title of talk  Congruences for tcore partitions).
 July 22  26, 2019: 15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA'19), Hagenberg, Austria (Title of talk  New Representations for $\sigma(q)$ via Reciprocity Theorems).
 July 29  Aug. 02, 2019: 5th Algorithmic and Enumerative Combinatorics Summer School (AEC'19), Hagenberg, Austria.
 Sept. 25  27, 2019: DK Statusseminar, Strobl, Austria.
 Oct. 25, 2019 : SFB Colloquium, TU Wien, Austria.
 Nov. 12, 2019: DK Computational Mathematics Seminar, JKU (Title of talk  BSP and Partition Identities).
 Nov. 20, 2019: Algorithmic Combinatorics Seminar, RISC, JKU (Title of talk  Inequalities of the Partition function).
 Dec. 08  11, 2019: SFB Statusseminar, Strobl, Austria.
 Jan. 31, 2020: SFB colloquium, RISC, Hagenberg, Austria.
 May 27, 2020: Algorithmic Combinatorics Seminar, RISC, JKU (via zoom) (Title of talk  A brief overview on William Chen's conjecture).
 June 02, 2020: DK Computational Mathematics Seminar, JKU (via zoom) (Title of talk  Inequalities of the partition function : an overview).
 Sept. 06  09, 2020: 85th Seminaire Lotharingien De Combinatoire (SLC'85), Strobl, Austria (Title of talk  Hook Type Tableaux and Partition Identities).
 Sept. 15  Sept. 16, 2020 : SFB QMC Workshop, JKU (via zoom).
 Sept. 24,2020: DK Statusseminar, JKU (via zoom)(Title of talk  A brief overview on inequalities of the partition function).
 Nov. 26, 2020: DK Computational Mathematics Seminar, JKU (via zoom) (Title of talk  Invariant theory and partition inequalities).
 Dec. 16, 2020: SFB Statusseminar (U. Wien T.U.WienJKU) (via zoom) (Title of talk  Bill Chen's conjectures on partition inequalities).
 Dec. 22, 2020: International Conference on Number Theory and Algebra (ICNTA'20), IIT BHU, Varanasi, India (held via online) (Ttitle of talk  Bill Chen's conjecture on partition inequalities).
 May 1014 and 1721, 2021: Hausdorff School: The Circle Method, Bonn, Germany (online).
 May 1216, 2021: Number Theory conference in Honor of Prof. R. Balasubramanian's 70th Birthday, IMSc, India (online).
 June 02, 2021: Algorithmic Combinatorics Seminar, RISC, JKU (via zoom) (Title of talk  Inequalities for the modified Bessel function of first kind of integral order).
 June 08, 2021: DK Computational Mathematics Seminar, JKU (via zoom) (Title of talk  Finer asymptotics and inequalities for partition function and its consequences).
 July 1216, 2021: Symposium on Number Theory, in honor of Prof. M. V. Subbarao on his birth centenary, IISER Pune, India (online).
 Nov. 25, 2021: Seminar Series: Topics in Special Functions and Number Theory (IIT, Gandhinagar  Ashoka Univ.  JNU) (via zoom) (Title of talk  Inequalities for the modified Bessel function of first kind and its consequences).
 Dec. 01, 2021: SFB Statusseminar (U. Wien  T. U. Wien  JKU) (via zoom) (Title of talk  Inequalities for the modified Bessel function of first kind).
 Jan. 12, 2022: Algorithmic Combinatorics Seminar, RISC, JKU (via zoom) (Title of Talk  Optimality for bounds of the modified Bessel function of first kind).
 Jan. 18, 2022: DK Computational Mathematics Seminar, JKU (via zoom) (Title of talk  Parity bias in partitions and restricted partitions).
 April 26, 2022: DK Computational Mathematics Seminar, JKU (Title of talk  Congruences for kelongated plane partitions modulo powers of 5).
 May 02, 2022: RISC Forum, RISC, JKU (Title of talk  Inequalities for the partition function).
 June 22, 2022: Algorithmic Combinatorics Seminar, RISC, JKU (Title of talk  Inequalities for special functions and sequences).
 July 04  08, 2022: Algorithmic and Enumerative Combinatorics, TU Wien, Austria.
 Oct. 27  29, 2022: DK Computational Mathematics Concluding Event, RICAM, JKU (Title of talk  Error bounds for the asymptotic expansion of the partition function and its consequences).
 Nov. 21  25, 2022: Workshop on Cylindric Partitions, RICAMRISC, JKU.
 Nov. 28, 2022: RISC Forum, RISC, JKU (Title of talk  New asymptotics and inequalities related to the partition function).
 Nov. 30, 2022: Algorithmic Combinatorics Seminar, RISC, JKU (Title of talk  New asymptotics and inequalities related to the partition function).
 Dec. 20  22, 2022: 18th International Conference on Srinivasa Ramanujan (SASTRA Ramanujan Conference), SASTRA Ramanujan Centre, SASTRA University, Kumbakonam, India (Title of talk  Error bounds for the asymptotic expansion of the partition function and its applications).
 Jan. 09, 2023: GANIT Seminar, IIT Gandhinagar, India (Title of talk  Error bounds for the asymptotic expansion of the partition function and its consequences).
Refereeing Activities
Reviewer for Bulletin of the Australian Mathematical Society, European Journal of Combinatorics, Journal of Number Theory, Online Journal of Analytic Combinatorics, Proceedings of the American Mathematical Society, Ramanujan Journal, Rocky Mountain Journal of Mathematics.
Awards
 2011  2016 : INSPIRE Scholarship, Department of Science and Technology, Government of India.
 2011  2014 : Central Sector Scheme of Scholarship for College and University Students, M.H.R.D, Department of Higher Education, Government of India.
Teaching
 Oct. 2021  Jan. 2022 : Teaching Assistant for Algebraic Combinatorics, Johannes Kepler University, Austria.
 Oct. 2020  Jan. 2021 : Teaching Assistant for Algebraic Combinatorics, Johannes Kepler University, Austria.
 Aug.Dec., 2017 : Teaching assistant for Combinatorics, Indian Institute of Science Education and Research, Tirupati, India.
