+91-674-249-4082

Submitted by jaban on 22 December, 2015 - 17:47

Designation:

Assistant Professor

Dean/Chairperson/Convenor/Warden:

Convener, UGCS

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:**

**Assistant Professor**(Since December, 2015), 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 S. Pujahari and K. D. Shankhadhar)
*Zeros of L-functions attached to cusp forms of half-integral weight*, accepted for publication in**Proc. Amer. Math. Soc**. - (With A. Kumar)
*Rankin-Cohen brackets and identities among eigenforms*, accepted for publication in**Pacific Journal of Mathematics**. - (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.

Preprints:

- (With B. Kumar and S. Pujahari)
*Some remarks on the coefficients of symmetric power L-functions*, submitted. - (With S. K. Singh) Mod p modular forms and simple congruences, submitted.
- (With A. Kumar) Rankin-Cohen brackets and identities among eigenforms II, preprint.

Teaching:

- M601-Algebra I (Fall-2017, Fall-2018), NISER
- M307- Field Theory (Spring-2016, Spring-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:

- UGCS Convener

Project/Thesis Guidance:

- M. Sc. Thesis of Jyotiraditya Singh, 2017, NISER.
- M. Sc. Thesis of Sourabhashis Das, 2018, NISER.
- Ph. D. Thesis of Sujeet Kumar Singh (continuing).

**Postdoctoral Fellows:**

- Arvind Kumar (September, 2017--July, 2018).

Academic Presentations:

, 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**

- 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**

- 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).

Sponsored Projects:

: Department of Science and Technology, Govt. of India,*Identities among eigenforms and zeros of certain L-functions (MTR/2017/000022),*Funding Agency**Duration**: 2018-2021.

Contact:

Office Phone:

0674-249-4097

Office address:

School of Mathematical Sciences, NISER, Bhubaneswar, P.O.: Bhimpur-Padanpur, Via- Jatni, Khurda- 752050, Odisha, India

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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