Designation

Associate Professor

Joining Date

Expiry of Tenure

Research Area

Number Theory

Education

**Ph. D., July, 2012**,*Harish-Chandra Research Institute*, Allahabad**M. Sc., 2006**,*Utkal University*, Bhubaneswar, Odisha**B. Sc., 2004**,*Gangadhar Meher (Autonomous) College, (Sambalpur University)*, Sambalpur, Odisha.

__ Professional Experiences:__

**Associate Professor**(July, 2022--), NISER, Bhubaneswar.**Reader-F**(July, 2018--June, 2022), NISER, Bhubaneswar.**Assistant Professor**(December, 2015--June, 2018), NISER, Bhubaneswar.**Inspire Faculty**(October, 2013--December, 2015), IISc, Bangalore.**Postdoctoral Fellow**(September, 2012--August, 2013), Queen's University, Canada.

Research Interest

Modular forms, L-functions

Awards

- Inspire faculty award by Department of Science and Technology (DST) in 2013 (Session-I).
- National Board for Higher Mathematics (NBHM) Research Fellowship, 2006 (did not avail).

Publications

- (With M. K. Pandey and K. D. Shankhadhar) Koecher-Maass series have infinitely many critical zeros,
**Bull. Lond. Math. Soc.,**to appear. - (With M. Tripathi)
_{4}F_{3}-Gaussian hypergeometric series and traces of Frobenius for elliptic curves,**Res. Math. Sci.,**9 (2022), - (With A. Kumar and K. D. Shankhadhar)
*On signs of Hecke eigenvalues of Siegel eigenforms,***Mathematika,**68 (2022), 1030--1044. - (With M. Charan, K. D. Shankhadhar and R. K. Singh)
*A converse theorem for quasimodular forms*,**Forum Math.,**34 (2022), 547--564. - (With S. K. Singh)
*Mod p modular forms and simple congruences*,**Ramanujan J.**, 56 (2021), 821--838. - (With A. Kumar and K. D. Shankhadhar)
*Strong multiplicity one for Siegel cusp forms of degree two*,**Forum Math.**, 33 (2021), 1157--1167. - (With S. K. Singh)
*Structure of Hermitian modular forms modulo p and some applications*,**Res. Number Theory**, - (With A. Kumar)
*Rankin-Cohen brackets and identities among eigenforms II,***Modular Forms and Related Topics in Number Theory,**125--141,**Springer Proceedings of Mathematics and Statistics, Vol. 340,**2020. - (With S. K. Singh)
*Congruences in Hermitian Jacobi and Hermitian modular forms*,**Forum Math.**, 32 (2020), 501--523. - (With B. Kumar and S. Pujahari)
*Some remarks on the coefficients of symmetric power L-functions,***Automorphic Forms and Related Topics**, 155--164,**Contemporary Mathematics, Vol. 732,**American Mathematical Society, 2019. - (With S. Pujahari and K. D. Shankhadhar)
*Zeros of L-functions attached to cusp forms of half-integral weight*,**Proc. Amer. Math. Soc.**, 147 (2019), 131--143. - (With A. Kumar)
*Rankin-Cohen brackets and identities among eigenforms,***Pacific Journal of Mathematics**, 297 (2018), 381--403. - (With K. D. Shankhadhar and G. K. Viswanadham)
*On the coefficients of symmetric power L-functions***,****Int. J. Number Theory,**14 (2018), 813--824. *On weakly holomorphic quasimodular forms**,***J. Ramanujan Math. Soc.,**32 (2017), 339--353.- (With S. Pujahari and K. Srinivas)
*Zeros of L-functions attached to modular forms of half-integral weight*,**Bull. Lond. Math. Soc.,**49 (2017), 926--936. - (With M. Ram Murty)
*Oscillations of coefficients of Dirichlet series attached to automorphic forms*,**Proc. Amer. Math. Soc**., 145 (2017), 563--575. - (With A. Kumar)
*On arbitrary products of eigenforms*,**Acta Arithmetica,**173 (2016), 283--295. - (With S. B. Sinha)
*Some infinite sums identities*,**Czechoslovak Math. J**., 65 (2015), 819--827. - (With K. D. Shankhadhar)
*Asymptotic formulas for the coefficients of certain automorphic functions*,**Acta Arithmetica**, 169 (2015), 59--76. - (With S. Pujahari and K. D. Shankhadhar)
*Sign changes of coefficients of certain Dirichlet series*,**Funct. Approx. Comment. Math.**, 52 (2015), 117--126. - (With M. Manickam and B. Ramakrishnan)
*Theory of newforms of half-integral weight*,**Pacific Journal of Mathematics**, 274 (2015), 125--139. - (With S. Das)
*On quasimodular eigenforms*,**Int. J. Number Theory**, 11 (2015), 835--842. - (With N. Tanabe)
*Sign changes of Fourier coefficients of Hilbert modular forms*,**J. Number Theory**, 145 (2014), 230--244. - (With M. Ram Murty)
*Sign changes of Fourier coefficients of half-integral weight cusp forms*,**Int. J. Number Theory**, 10 (2014), 905--914. *Some remarks on zeros of quasimodular forms*,**Arch. Math. (Basel)**, 101 (2013), 121--127.- (With K. D. Shankhadhar and G. K. Viswanadham)
*A short note on sign changes*,**Proc. Indian Acad. Sci. Math. Sci**, 123 (2013), 315--320. - (With M. Ram Murty)
*Ramanujan's proof of Bertrand's postulate*,**Amer. Math. Monthly**, 120 (2013), 650--653. *Some remarks on Rankin-Cohen brackets of eigenforms*,**Int. J. Number Theory**, 8 (2012), 2059--2068.- (With W. Kohnen)
*Some remarks on the q-exponents of generalized modular functions*,**Ramanujan J.**, 25 (2011), no.1, 115--119.

Teaching

- MA602-Algebra-II (Fall-2021, Spring-2023), NISER
- M471-Advanced Number Theory (Fall-2022), NISER
- MA601-Algebra-I (Spring-2022), NISER
- M307-Field Theory (Spring-2016, Spring-2018, Spring-2019, Spring-2021), NISER
- M101-Mathematics-I (Fall-2020), NISER
- M552-Analytic Number Theory (Spring-2020), NISER
- M403-Commutative Algebra (Fall-2019), NISER
- M601-Algebra I (Fall-2017, Fall-2018), NISER
- M560-Modular forms of one variable (Spring-2017), NISER
- M302-Rings and Modules (Fall-2016), NISER
- MA 215-Introduction to Modular forms (Fall-2015), IISc, Bangalore
- MATH 311-Elementary Number Theory (Fall-2012), Queen's University, Kingston, Canada

Responsibility

- Hostel Warden (2016-2017).
- UGCS Convener (2016-2018).
- Member, PGCS, SMS (2018-2020, 2022-)
- Member, UGCS, SMS (2020-2022)

Project/Thesis Guidance

- M. Sc. Thesis of Jyotiraditya Singh, 2017, NISER.
- M. Sc. Thesis of Sourabhashis Das, 2018, NISER.
- M. Sc. Thesis of Anshada P M (continuing).
- Ph. D. Thesis of Sujeet Kumar Singh, June 2020, NISER.
- Ph. D. Thesis of Mrityunjoy Charan (continuing).

__Postdoctoral Fellows:__

- Arvind Kumar (September, 2017--July, 2018).
- Ritwik Pal (January--July, 2021).
- Lalit Vaishya (December, 2021--September, 2022).
- Mohit Tripathi (April, 2021--).

Academic Presentations

National seminar on mathematics analysis and its applications, Kendrapada Autonomous College, Kendrapada, Odisha (18--19 March, 2023).**Ramanujan tau function,**Kendrapada Autonomous College, Kendrapada, Odisha (27 February, 2023).**Euler Phi-function,**National workshop on Role of Mathematics in Science and Emerging Technology, Sri Sri University, Cuttack, (20 January, 2023).**On solving polynomial equations,**NCM workshop on Jacobi forms, IIT Guwahati, (12--24 December, 2022).**On the theory of Jacobi forms,**IIT Jammu, 9 & 11 November, 2022.*An introduction to modular forms,*L-functions, circle method and applications, ICTS, Bengaluru, (27 June--1 July, 2022).**Zeros of L-functions attached to half-integral weight modular Forms,**(Online) Seminar in Special Functions and Number Theory, 30 September, 2021.**Modular forms and certain congruences,**Modular forms, An online conference in honour of Prof. B Ramakrishnan's 60th birthday, (17--19 September, 2021).**Converse theorem for quasimodular forms,**L. N. College, Jharsuguda, Odisha (online talk) (9 January, 2021).**Euler Phi-function,**International conference on Number theory and Algebra (online meeting), IIT (BHU), Varanasi, (22--23 December, 2020).**Mod p modular forms and simple congruences,**Chandrasekharan centenary symposium in number theory, 86th Annual conference of Indian Mathematical Society (online meeting), VIT Vellore, (17--20 December, 2020).**Mod p modular forms and simple congruences,**, IISER Bhopal Math Symposium, IISER Bhopal,(6--7 March, 2020).**Certain congruences among Hermitian Jacobi forms**, International Conference on Number Theory, Kerala School of Mathematics, Kozhikode, (23--26 January, 2020).**Certain congruences among Hermitian Jacobi forms**, Harish Chandra Research Institute, Prayagraj, (4 January, 2020).*Theory of newforms of half-integral weight*, Institute of Mathematics and Applications, Bhubaneswar, (22 December, 2019).**Some of the works of Ramanujan**NCERT-NTS awardees nurturance program, NISER, Bhubaneswar, (9-13 December, 2019).**Prime numbers and some questions,**, National seminar on recent trends in mathematical analysis and applications, Utkal University, Bhubaneswar, India, (28 February-1 March, 2019).*Distribution of the signs of the Fourier coefficients of certain modular forms*, 16th International conference on Srinivasa Ramanujan, Srinivasa Ramanujan Centre, SASTRA deemed to be University, Kumbakonam, India, (21-22 December, 2018).**Certain identities among eigenforms**, Conference on Number Theory, Kerala School of Mathematics, Kozhikode, India, (10--14 December, 2018).**Certain identities among eigenforms**, Workshop on Modular forms, Kerala School of Mathematics, Kozhikode, India, (12--14 October, 2018).**On the coefficients of symmetric power L-functions**, Building Bridges: 4th EU/US Workshop on Automorphic forms and Related topics, Alfred Renyi Institute of Mathematics, Budapest, Hungary (14-20 July, 2018).*Certain identities among eigenforms*, School on Modular forms, Kerala School of Mathematics, Kozhikode, India, (22--24 February, 2018).*Rankin-Cohen brackets and identities among eigenforms*, Number theory: Arithmetic, Diophantine and Transcendence, IIT Ropar, India, (22--25 December, 2017).**Rankin-Cohen brackets and identities among eigenforms**, 31st Automorphic forms workshop, East Tennessee State University, Johnson City, Tennessee, USA, (6–9 March, 2017).*Zeros of L-functions attached to half-integral weight cusp forms*, Inspire Faculty Monitoring-cum-Interaction Meet (27 January, 2017), Goa University, India.**Quasimodular forms**, Building Bridges: 3rd EU/US Workshop on Automorphic forms and Related topics, University of Sarajevo, Sarajevo, Bosnia & Herzegovina, (18-22 July, 2016).**Zeros of L-functions attached to half-integral weight cusp forms**, 30th Automorphic forms workshop, Wake Forest University, Winston-Salem, North Carolina, USA, (7–10 March, 2016).**Products of Eigenforms***Zeros of L*, Workshop on Automorphic forms, Kerala School of Mathematics, Kozhikode, India, (10–16 February, 2016).*-functions attached to half-integral weight cusp forms***Asymptotic formulas for the coefficients of certain modular functions**, Dept.of Mathematics, IIT Delhi, New Delhi, India (27th April 2015).**Products of eigenforms****,**Dept. of Mathematics, IIT Kanpur, India (19th March 2015)., International conference on Automorphic forms, Kerala School of Mathematics, Kozhikode, India, (13-14 February, 2015).**Asymptotic formula for the coefficients of weakly holomorphic quasimodular forms**, Workshop on Jacobi forms and Modular forms of half-integral weight, Kerala School of Mathematics, Kozhikode, India, (2-12 February, 2015).**Product of eigenforms****Asymptotic formulas for the coefficients of certain modular functions**, Dept. of Mathematics, IIT Madras, Chennai, India (21st January 2015).**Products of eigenforms**, Mathematics Seminar, NISER, Bhubaneswar, India (13th October 2014)., Advanced Instructional School on Algebraic Number Theory, Chennai Mathematical Institute, Chennai (7-26 July, 2014).**Cyclotomic fields**, International Conference on Automorphic Forms and Number Theory, Kerala School of Mathematics, Kozhikode, (2-3 September, 2013).**Zeros of quasimodular forms****Zeros of quasimodular forms**, Number Theory Seminar, Queen’s University, Canada, (26th June 2013).**Zeros of quasimodular forms**, IISER, Bhopal, India (through Skype), (12th June 2013).**Sign changes of the Fourier coefficients of half-integral weight cusp forms in Kohnen’s plus space**, Number Theory Seminar, Queen’s University, Canada, (8th March 2013).**Sign changes of the Fourier coefficients of half-integral weight modular forms**, Number Theory Seminar, Queen’s University, Canada, (9th November 2012).**Product of eigenforms**, Number Theory Seminar, Queen’s University, Canada, (5th October 2012).**Some problems on modular forms**, HRI, Allahabad, (July 2012)., Theory of Prime numbers and Related Areas, Kerala School of Mathematics, Kozhikode, India, (6-10 May, 2012).**Products of eigenforms****Set of three lectures on Modular forms**, ATM School for Lecturers in Number Theory, HRI, Allahabad, (December 2011).**On generalized modular forms**, HRI, Allahabad, (August 2011)., ICM Satellite Conference on Modular forms, Mahabalipuram (near Chennai), India, (1-9 August, 2010).**On generalized modular functions****On Sard’s theorem**, HRI, Allahabad, (May 2007).**Distribution of residues modulo p**, HRI, Allahabad, (December 2006).

Academic Visits

__Conferences/Schools/Workshops Attended__- NCM workshop on Jacobi forms, (12--24 December, 2022), IIT Guwahati, India.
- L-functions, circle method and applications, (27 June--1 July, 2022), ICTS, Bengaluru, India.
- Modular forms, An online conference in honour of Prof. B Ramakrishnan's 60th birthday, (17--19 September, 2021).
- Online Workshop on Modular Forms (14--19 December, 2020), IIT Guwahati, India.
- IISER Bhopal Math Symposium (6--7 March, 2020), IISER Bhopal, India.
- International conference on Number Theory (23--26 January, 2020), International Conference on Number Theory, Kerala School of Mathematics, Kozhikode, India.
- Discussion meeting on Sphere Packing (31 October--6 November, 2019), ICTS, Bengaluru, India.
- National seminar on recent trends in mathematical analysis and applications (28 February-1 March, 2019), Utkal University, Bhubaneswar, India.
- 16th International conference on Srinivasa Ramanujan (21-22 December, 2018), Srinivasa Ramanujan Centre, SASTRA deemed to be University, Kumbakonam, India.
- Conference on Number Theory (10-14 December, 2018), Kerala School of Mathematics, Kozhikode, India.
- Workshop on Number Theory (30 November--6 December, 2018), NISER, Bhubaneswar, India.
- Workshop on Modular forms (12-14 October, 2018), Kerala School of Mathematics, Kozhikode, India.
- Building Bridges: 4th EU/US Summer School + Workshop on Automorphic forms and Related topics (9-20 July, 2018), Alfred Renyi Institute of Mathematics, Budapest, Hungary.
- School on Modular forms (22-24 February, 2018), Kerala School of Mathematics, Kozhikode, India.
- Number theory: Arithmetic, Diophantine and Transcendence (22-25 December, 2017), IIT Ropar, India.
- 31st Automorphic forms workshop (6-9 March, 2017), East Tennessee State University, Johnson City, Tennessee, USA.
- Inspire Faculty Monitoring-cum-Interaction Meet (27 January, 2017), Goa University, India.
- School and Workshop on Modular forms and Black holes (5--14 January, 2017), NISER, Bhubaneswar, India.
- Discussion meeting on Automorphic forms (21--27 December, 2016), NISER, Bhubaneswar, India.
- Number Theory conference on Arithmetic Geometry and L-functions (17--21 August, 2016), Kerala School of Mathematics, Kozhikode, India.
- Building Bridges: 3rd EU/US Summer School + Workshop on Automorphic forms and Related topics (11-22 July, 2016), University of Sarajevo, Sarajevo, Bosnia & Herzegovina.
- 30th Automorphic forms workshop (7-10 March, 2016), Wake Forest University, Winston-Salem, North Carolina, USA.
- Workshop on Automorphic forms (10–16 February, 2016), Kerala School of Mathematics, Kozhikode, India.
- ATM Workshop in Analytic Number Theory (19–24 October, 2015), IMSc, Chennai.
- Advanced Instructional School in Analytic Number Theory (1–20 June, 2015), KIIT University, Bhubaneswar, India.
- International conference on Automorphic forms (13-14 February, 2015), Kerala School of Mathematics, Kozhikode, India.
- Workshop on Jacobi forms and Modular forms of half-integral weight (2-12 February, 2015), Kerala School of Mathematics, Kozhikode, India.
- Winter school on Modular functions in one and several variables (8-17 December, 2014), Goa University, Goa, India.
- Advanced School and Workshop on L-functions and modular forms (1-12 September, 2014), ICTP, Trieste, Italy.
- International Congress of Mathematicians (13-21 August, 2014), Seoul, South Korea.
- Advanced Instructional School in Algebraic Number Theory (7-26 July, 2014) Chennai Mathematical Institute, Chennai.
- Conference on Analytic Theory of Automorphic Forms (9-13 December, 2013), IMSc, Chennai.
- International Conference on Automorphic Forms and Number Theory (2-3 September, 2013), Kerala School of Mathematics, Kozhikode, India.
- Theory of Prime numbers and Related Areas (6-10 May, 2012), Kerala School of Mathematics, Kozhikode, India.
- International Colloquium on Automorphic representations and L-functions (3-11 January, 2012), TIFR, Mumbai.
- International Meeting on Number Theory, celebrating the 60th Birthday of Professor R. Balasubramanian (15-20 December, 2011), HRI, Allahabad.
- School and Conference on Modular forms and Mock Modular forms and their Applications in Arithmetic, Geometry and Physics (28 February-18 March, 2011), ICTP, Trieste, Italy.
- IISER-KOLKATA Winter School on Number Theory (Waring’s Problem) (13-17 December, 2010), IISER, Kolkata.
- ICM Satellite Conference on Analytic and Combinatorial Number Theory (29 August-3 September, 2010), IMSc, Chennai.
- International Congress of Mathematicians (19-27 August, 2010), Hyderabad, India.
- ICM Satellite Conference on Modular forms (1-9 August, 2010), Mahabalipuram (near Chennai).
- Besse Summer School on Quasimodular forms (20-26 June, 2010), Besse et Saint-Anastaise, France.
- Workshop on Theory of Jacobi forms and Siegel modular forms (23 November- 5 December, 2009), RKM Vivekananda College and IMSc, Chennai.
- SMS 2009, Automorphic forms and L-functions: computational aspects (22 June-3 July, 2009), Universite de Montreal, Montreal, Canada.
- HRI International Conference in Mathematics (March, 2009), HRI, Allahabad.
- Discussion Meeting on Modular Forms (21 February-6 March, 2009), HRI, Allahabad.
- Workshop on Compact Lie groups and their Representations (17-29 November, 2008), HRI, Allahabad.
- Workshop on Elliptic curves and their Applications (21 July-2 August, 2008), IMSc, Chennai.
- Advanced Instructional School in Algebraic and Analytic Number Theory (3- 28 December, 2007), HRI, Allahabad.
- International Conference on Number Theory and Cryptography (23-27 February 2007), HRI, Allahabad.
- International Conference on Number Theory (1-5 December,2006), HRI, Allahabad.

__Institutes Visited__

- IIT Jammu (November 2022)
- IISER Bhopal (March 2020).
- Kerala School of Mathematics, Kozhikode, Kerala (December 2013, May 2014, September 2014, February 2015).
- The Institute of Mathematical Sciences, Chennai (September-October 2013, January 2015).
- Harish-Chandra Research Institute, Allahabad (April 2014, March 2015, May-June 2019, January 2020, February 2020).

Sponsored Projects

: Science & Engineering Research Board (SERB), Department of Science and Technology, Government of India,*Identities among eigenforms and zeros of certain L-functions (MTR/2017/000022),*Funding Agency**Amount:**Rs. 6,60,000,**Duration**: 2018-2021.**Structure of Hermitian modular forms modulo p and mod p kernel of theta function (CRG/2020/004147),****Funding Agency:**Science & Engineering Research Board (SERB), Department of Science and Technology, Government of India,**Amount:**Rs. 30,41,544,**Duration:**2020-2023.