Publications

1. Zeros of combinations of Riemann Ξ-function and confluent Hypergeometric Function on bounded vertical shifts 

     (joint work with Atul Dixit, Bibekananda Maji, and Alexandru Zaharescu),  Journal of Mathematical Analysis and Applications, 466 (2018), 307-323.  

DOI: https://doi.org/10.1016/j.jmaa.2018.05.072

2. Generalized Lambert series, Raabe's Cosine Transform and a generalization of Ramanujan formula's for ζ(2m+1) 

    (joint work with Atul Dixit, Rajat Gupta, and Bibekananda Maji),  Nagoya Mathematical Journal, 239 (2020), 232–293.

DOI: https://doi.org/10.1017/nmj.2018.38

3. The generalized modified Bessel function and its connection with Voigt line profile and Humbert functions 

    Rahul Kumar,  Advances in Applied Mathematics, 114 (2020), 101986, 19 pp.

DOI: https://doi.org/10.1016/j.aam.2019.101986

4. On Hurwitz zeta function and Lommel functions 

    (Joint work with Atul Dixit) ,  International Journal of Number Theory, Vol. 17, No. 2 (2021) 393–404, 

  DOI: https://doi.org/10.1142/S1793042120400047.

5. Superimposing theta structure on a generalized modular relation 

     (Joint work with Atul Dixit),  Research in the Mathematical Sciences, 8,  pp 01-83, Article number: 41 (2021).

     DOI: https://doi.org/10.1007/s40687-021-00277-0

6. On some q-series identities related to the generalized divisor function and their implications 

    (Joint work with Rajat Gupta), Discrete Mathematics,  344 (2021), no. 11, Paper No. 112559, 21 pp.

    DOI: https://doi.org/10.1016/j.disc.2021.112559 .

7. Explicit transformations of certain Lambert series 

    (Joint work with Atul Dixit and Aashita Kesarwani),  Research in the Mathematical Sciences, 9,  pp 01-54, Article number: 34 (2022).

 DOI: https://doi.org/10.1007/s40687-022-00331-5

8. Extensions of Watson's theorem and the Ramanujan-Guinand formula 

    Rahul Kumar,  International Journal of Number Theory, Vol. 19, No. 1 (2023) 199–222.

   DOI: https://doi.org/10.1142/S1793042123500082

9.  Extended higher Herglotz functions I. Functional equations 

        (Joint work with Atul Dixit and Rajat Gupta),  Advances in Applied Mathematics, Volume 153, February 2024, 102622, pp 01--41.

   DOI: https://doi.org/10.1016/j.aam.2023.102622

10. Equivalent criterion for the grand Riemann hypothesis associated to Maass cusp forms 

        (Joint work with Soumyarup Banerjee), to appear in Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, 16 pages.

        DOI: https://doi.org/10.1017/prm.2023.66

11.  Extended Higher Herglotz function II 

         (Joint work with Rajat Gupta),  Journal of Mathematical Analysis and  Applications, 518 no. 2 (2023), Paper No. 126720 (16 pages).

       DOI: https://doi.org/10.1016/j.jmaa.2022.126720

12. A modular relation involving a generalized digamma function and asymptotics of some integrals containing Ξ(t)

     (Joint work with Atul Dixit ),  Hardy-Ramanujan Journal, 45 (2022), 140--151.

    DOI: https://doi.org/10.46298/hrj.2023.10913

13. Arithmetic properties of the Herglotz-Zagier-Novikov function 

     (Joint work with YoungJu Choie), Advances in Mathematics, Volume 433, 15 November 2023, 109315, pp 01--36.

       DOI: https://doi.org/10.1016/j.aim.2023.109315

14. Applications of the Lipschitz summation formula and a generalization of Raabe's cosine transform 

     (Joint work with Atul Dixit ), to appear in Constructive Approximation, pp 01--40, 2023.

    DOI: https://doi.org/10.1007/s00365-023-09668-8

15. A note on odd zeta values over any number field and Extended Eisenstein series

     (Joint work with Soumyarup Banerjee and Rajat Gupta), Journal of Mathematical Analysis and  Applications, 531 (2024) 127883, pp 01--17.   

    DOI: https://doi.org/10.1016/j.jmaa.2023.127883 

16.  Explicit identities on zeta values over imaginary quadratic field 

     (Joint work with Soumyarup Banerjee), Submitted for publication.

17.  Number field analogue of divisor function à la Koshliakov 

       (Joint work with Soumyarup Banerjee), Submitted for publication.

18.  Kronecker second limit formula for real quadratic fields

     (Joint work with YoungJu Choie), Submitted for publication, pp 01--34.

19.  Kronecker's limit formulas and their applications

      (Joint work with YoungJu Choie), under preparation.