
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
- Professor Gokulananda Das research award in Mathematics-2023.
- 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., 55 (2023), 2224--2232.
- (With M. Tripathi) 4F3-Gaussian hypergeometric series and traces of Frobenius for elliptic curves, Res. Math. Sci., 9 (2022), Article no. 63.,
- (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, 7 (2021), Article no. 52.
- (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
- M305/MA703-Number Theory (Fall-2023), NISER
- 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, 2023, NISER.
- Ph. D. Thesis of Sujeet Kumar Singh, June 2020, NISER.
- Ph. D. Thesis of Mrityunjoy Charan, August 2023, NISER.
Postdoctoral Fellows:
- Arvind Kumar (September, 2017--July, 2018).
- Ritwik Pal (January--July, 2021).
- Lalit Vaishya (December, 2021--September, 2022).
- Mohit Tripathi (April, 2021--August, 2023).
- Sandeep E. M. (June, 2023--).
Academic Presentations
- Euler's phi function and some applications, NISER outreach teachers' training workshop, NISER Bhubaneswar (25--28 September, 2023).
- Determination of Siegel modular forms from their Hecke eigenvalues, Mathematics days, NISER, Bhubaneswar (8--9 September, 2023).
- Ramanujan tau function, National seminar on mathematics analysis and its applications, Kendrapada Autonomous College, Kendrapada, Odisha (18--19 March, 2023).
- Euler Phi-function, Kendrapada Autonomous College, Kendrapada, Odisha (27 February, 2023).
- On solving polynomial equations, National workshop on Role of Mathematics in Science and Emerging Technology, Sri Sri University, Cuttack, (20 January, 2023).
- On the theory of Jacobi forms, NCM workshop on Jacobi forms, IIT Guwahati, (12--24 December, 2022).
- An introduction to modular forms, IIT Jammu, (9 & 11 November, 2022).
- Zeros of L-functions attached to half-integral weight modular Forms, L-functions, circle method and applications, ICTS, Bengaluru, (27 June--1 July, 2022).
- On Ramanujan tau function, Webinar on Number Theory, Utkal University, (29 December, 2021).
- Modular forms and certain congruences, (Online) Seminar in Special Functions and Number Theory, 30 September, 2021.
- Converse theorem for quasimodular forms, Modular forms, An online conference in honour of Prof. B Ramakrishnan's 60th birthday, (17--19 September, 2021).
- Euler Phi-function, L. N. College, Jharsuguda, Odisha (online talk) (9 January, 2021).
- Mod p modular forms and simple congruences, 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).
- Certain congruences among Hermitian Jacobi forms, 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).
- Theory of newforms of half-integral weight, Harish Chandra Research Institute, Prayagraj, (4 January, 2020).
- Some of the works of Ramanujan, Institute of Mathematics and Applications, Bhubaneswar, (22 December, 2019).
- Prime numbers and some questions, NCERT-NTS awardees nurturance program, NISER, Bhubaneswar, (9-13 December, 2019).
- Distribution of the signs of the Fourier coefficients of certain modular forms, National seminar on recent trends in mathematical analysis and applications, Utkal University, Bhubaneswar, India, (28 February-1 March, 2019).
- Certain identities among eigenforms, 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).
- On the coefficients of symmetric power L-functions, Workshop on Modular forms, Kerala School of Mathematics, Kozhikode, India, (12--14 October, 2018).
- Certain identities among eigenforms, Building Bridges: 4th EU/US Workshop on Automorphic forms and Related topics, Alfred Renyi Institute of Mathematics, Budapest, Hungary (14-20 July, 2018).
- Rankin-Cohen brackets and 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).
- Zeros of L-functions attached to half-integral weight cusp forms, 31st Automorphic forms workshop, East Tennessee State University, Johnson City, Tennessee, USA, (6–9 March, 2017).
- Quasimodular forms, Inspire Faculty Monitoring-cum-Interaction Meet (27 January, 2017), Goa University, India.
- Zeros of L-functions attached to half-integral weight cusp forms, Building Bridges: 3rd EU/US Workshop on Automorphic forms and Related topics, University of Sarajevo, Sarajevo, Bosnia & Herzegovina, (18-22 July, 2016).
- Products of Eigenforms, 30th Automorphic forms workshop, Wake Forest University, Winston-Salem, North Carolina, USA, (7–10 March, 2016).
- Zeros of L-functions attached to half-integral weight cusp forms, Workshop on Automorphic forms, Kerala School of Mathematics, Kozhikode, India, (10–16 February, 2016).
- 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).
- Asymptotic formula for the coefficients of weakly holomorphic quasimodular forms, International conference on Automorphic forms, Kerala School of Mathematics, Kozhikode, India, (13-14 February, 2015).
- Product of eigenforms, Workshop on Jacobi forms and Modular forms of half-integral weight, Kerala School of Mathematics, Kozhikode, India, (2-12 February, 2015).
- 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).
- Cyclotomic fields, Advanced Instructional School on Algebraic Number Theory, Chennai Mathematical Institute, Chennai (7-26 July, 2014).
- Zeros of quasimodular forms, International Conference on Automorphic Forms and Number Theory, Kerala School of Mathematics, Kozhikode, (2-3 September, 2013).
- 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).
- Products of eigenforms, Theory of Prime numbers and Related Areas, Kerala School of Mathematics, Kozhikode, India, (6-10 May, 2012).
- 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).
- On generalized modular functions, ICM Satellite Conference on Modular forms, Mahabalipuram (near Chennai), India, (1-9 August, 2010).
- On Sard’s theorem, HRI, Allahabad, (May 2007).
- Distribution of residues modulo p, HRI, Allahabad, (December 2006).
Academic Visits
Conferences/Schools/Workshops Attended
- Inter IISER-NISER Mathematics Meet-2023, (29 September--1 October, 2023), NISER, Bhubaneswar, India.
- 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, April 2023).
- 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
- Identities among eigenforms and zeros of certain L-functions (MTR/2017/000022), Funding Agency: Science & Engineering Research Board (SERB), Department of Science and Technology, Government of India, 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.