Dr. Anup Kumar Singh
Assistant Professor
Department of Mathematics,
Faculty of Science,
University of Allahabad (UoA),
Prayagraj - 211002,
Uttar Pradesh, India.
Emails:
anupsingh@allduniv.ac.in
anupsinghmath@gmail.com
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Arise, awake, and stop not till the goal is reached..(Swami Vivekananda)
Research Interest: Number Theory, Modular Forms (integer and half-integer weight), Representations of Numbers by Quadratic Forms, Partition function and Related Congruence, Convolution sums of divisor functions.
Publications:
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, Explicit evaluation of triple convolution sums of divisor functions, Int. J. Number Theory, 20(4), 1073–1098, (2024). (Link)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, A simple extension of Ramanujan-Serre derivative map and some applications, the Ramanujan J., 61, (2023), 1379 -- 1410. (Link)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, Representations of squares by certain diagonal quadratic forms in an odd number of variables, Rocky Mountain J. Math., 53(4), (2023), 1219 -- 1244. (Link)
Ankush Goswami, Abhash Kumar Jha and Anup Kumar Singh, Some identities for the partition function, J. Math. Anal. Appl., 508(1), (2022), 125864. (Link)
Anup Kumar Singh and Dongxi Ye, Ramanujan–Mordell type formulas associated to certain quadratic forms of discriminant 20k and 32k, Indian J. Pure Appl. Math., 51(3), (2020), 1083 --1096. (Link)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations of a natural number by certain quaternary quadratic forms, (Modular Forms and Related Topics in Number Theory), Springer Proc. Math. and Stat. 340 (2020) 173 -- 198. (Link)
Manish Kumar Pandey, B. Ramakrishnan and Anup Kumar Singh, Shimura and Shintani liftings on certain subspace of cusp forms of half-integral weight, Tsukuba J. Math., 43(2), (2019), 191 -- 210. (Link)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations of certain quadratic forms in 8 variables, Contemp. Math. (AMS), 732 (2019), 215 -- 224. (pdf) (sage-worksheet)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations by certain octonary quadratic forms with coefficients 1, 2, 3, 4 and 6, Int. J. Number Theory, 14, 751–812, (2018). (pdf)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, Representations of an integer by some quaternary and octonary quadratic forms, Geometry, Algebra, Number Theory and their Information Technology Applications (GANITA), Springer Proc. Math. and Stat. 251 (2018) 383 -- 409. (pdf)
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function, Funct. Approx. Comment. Math., 58 (2018), 233-244. (pdf).
B. Ramakrishnan, Brundaban Sahu and Anup Kumar Singh, On the representations of a positive integer by certain classes of quadratic forms in eight variables, Analytic Number Theory, modular forms and q- hypergeometric series, Springer Proc. Math. Stat., 221 (2017), 641–664. (pdf)
Education & Employment:
Assistant Professor (June 2023 -- ): University of Allahabad, Prayagraj, Uttar Pradesh.
NBHM Postdoctoral Fellow (May 2023 - June 2023): IIT(BHU) Varanasi, Uttar Pradesh.
Postdoctoral Fellow (Jan 2021 - April 2023): NISER Bhubaneshwar, Odisha.
Postdoctoral Research Fellow (Jun 2019 - Dec 2020): IISER Berhampur, Odisha.
Ph.D. (2019): Harish-Chandra Research Institute Prayagraj, Uttar Pradesh.
M.Sc. (2012): Banaras Hindu University (BHU) Varanasi, Uttar Pradesh.
B.Sc. (2010): St. Andrew's College Gorakhpur, Uttar Pradesh.
Teachings:
PG : MAT504 (Measure & Integration), University of Allahabad, Jan - May, 2025.
UG-III : Advanced Analysis, University of Allahabad, 2024 - 2025.
UG-II : Analysis, University of Allahabad, 2024 - 2025.
UG-I : Elementary Analysis, University of Allahabad, 2024 - 2025.
PG : MAT504 (Measure & Integration), University of Allahabad, Jan - May, 2024.
UG-II : Analysis, University of Allahabad, 2023 - 2024.
UG-I : Elementary Analysis, University of Allahabad, 2023 - 2024.
UG-I : Geometry, University of Allahabad, 2023 - 2024.
MTH305 (Elementary Number Theory), IISER Berhampur, Fall 2020.
MTH304 (Metric spaces and Topology), IISER Berhampur, Spring 2020.
MTH305 (Elementary Number Theory), IISER Berhampur, Fall 2019.
Tutorials:
M102 (An introduction to Real Analysis), NISER Bhubaneshwar, Jan - April 2023.
M101 (General Mathematics I), NISER Bhubaneshwar, Oct 2021 - Feb 2022.
M102 (An introduction to Real Analysis), NISER Bhubaneshwar, Feb - July 2021.
Annual Foundation School (AFS-II), NISER Bhubaneshwar, June 06 - July 02, 2022.
Instructional School for Teachers (IST) - Analytic Number Theory, IISER Berhampur, Dec 02 - Dec 14, 2019.
Awards and Fellowships:
NBHM Postdoctoral Fellowship (2023)
HRI-INFOSYS PRIZE (2018)
CSIR-JRF (AIR-10, 2013)
GATE (AIR-102, 2013)
NBHM-JRF (2013)
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