Jaban Meher

Designation

Associate Professor

Joining Date

08/12/2015

Expiry of Tenure

31/03/2049

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) 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

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

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).
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

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).

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