Research Interests
Analytic Number Theory, Special Functions, q-series, Partitions and Modular Forms
BioSketch
Research
Zeros of combinations of the Riemann Ξ-function and the confluent hypergeometric function on bounded vertical shifts
2018
A. Dixit, R. Kumar, B. Maji, A. Zaharescu | Elsevier
Journal: Journal of Mathematical Analysis and Applications, Pages: 307--323 , Volumes: 466 ,
Generalized Lambert series, Raabe’s cosine transform and a generalization of Ramanujan’s formula for ζ(2m + 1)
2020
Atul Dixit, Rajat Gupta, Rahul Kumar and Bibekananda Maji | Cambridge University Press
Journal: Nagoya Mathematical Journal
Superimposing theta structure on a generalized modular relation
2021
Atul Dixit and Rahul Kumar | Springer
Journal: Research in the Mathematical Sciences
A modular relation involving a generalized digamma function and asymptotics of some integrals containing Ξ(t)
2022
A. Dixit and R. Kumar | episciences
Journal: Hardy-Ramanujan Journal
The generalized modified Bessel function and its connection with Voigt line profile and Humbert functions
2020
R. Kumar | Elsevier
Journal: Advances in Applied Mathematics Pages: 01--19 , Volumes: 114 ,
On Hurwitz zeta function and Lommel functions
2021
A. Dixit and R. Kumar | World Scientific
Journal: International Journal of Number Theory Pages: 393–404 , Volumes: 2017 ,
On some q-series identities related to the generalized divisor function and their implications
2021
R. Gupta and R. Kumar | elsevier
Journal: Discrete Mathematics
Explicit transformations of certain Lambert series
2022
A. Dixit, A. Kesarwani and R. Kumar | Springer
Journal: Research in the Mathematical Sciences
Extensions of Watson’s theorem and the Ramanujan-Guinand formula
2023
R. Kumar | World Scientific
Journal: International Journal of Number Theory
Extended higher Herglotz functions II
2023
R. Gupta and R. Kumar | Elsevier
Journal: Journal of Mathematical Analysis and Applications
Extended higher Herglotz functions I. Functional equations
2024
A. Dixit, R. Gupta and R. Kumar | Elsevier
Journal: Advances in Applied Mathematics
A note on odd zeta values over any number field and Extended Eisenstein series
2024
S. Banerjee, R. Gupta and R. Kumar | Elsevier
Journal: Journal of Mathematical Analysis and Applications
A family of integrals related to values of the Riemann zeta function
2024
R. Kumar, Paul Levrie, Jean-Christophe Pain and Victor Scharaschkin | World Scientific
Journal: International Journal of Number Theory
Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms
2024
Soumyarup Banerjee and Rahul Kumar | Royal Society of Edinburgh
Journal: Proceedings of the Royal Society of Edinburgh, Section A: Mathematics
Arithmetic properties of the Herglotz-Zagier-Novikov function
2023
YoungJu Choie and Rahul Kumar | ScienceDirect
Journal: Advances in Mathematics
On Euler's Partition Theorem
2026
George Andrews, Rahul Kumar and Ae Ja Yee | AIMS
Journal: Frontiers in Combinatorics and Number Theory Pages: 26--30 , Volumes: 01 ,
Period function of Maass forms from Ramanujan's Lost notebook
2025
YoungJu Choie and Rahul Kumar | Elsevier
Journal: Advances in Mathematics Pages: 01--36 , Volumes: 474 ,
Explicit identities on zeta values over imaginary quadratic field
2025
Soumyarup Banerjee and Rahul Kumar | Springer
Journal: Advances in Applied Mathematics Pages: 01--42 , Volumes: 166 ,
Rank, two-color partitions and Mock theta functions
2025
George Andrews and Rahul Kumar | The American Mathematical Society
Journal: Proceedings of the American Mathematical Society, Pages: 4669--4682 , Volumes: 153 ,
Applications of the Lipschitz summation formula and a generalization of Raabe’s cosine transform
2024
Atul Dixit and Rahul Kumar | Springer
Journal: Constructive Approximation
Kronecker second limit formula for real quadratic fields
2026
YoungJu Choie and Rahul Kumar | Springer
Journal: Mathematische Annalen, Pages: 01--43 , Volumes: 394 ,
Honors And Awards
Teaching Engagements
