Anuj Jakhar
Associate Professor
Department of Mathematics
Indian Institute of Technology Madras
Postdoc fellows

  1. Dr. Mahesh Kumar Ram (Nov. 2024 –)
  2. Dr. Naveen Kumar (June 2025 –)
  3. Dr. Anubhav Sharma (March 2026 – June 2026)


Ph.D. Students

  1. Mr. Abhradeep Rakshit (jointly with Prof. Santanu Sarkar, IIT Madras) (Jan 2026–)
  2. Ms. Ankana Bhar (jointly with Prof. Santanu Sarkar, IIT Madras) (Jan 2026–)
  3. Mr. Karthik V Pai, IIT Madras (Jan 2026–)
  4. Mr. Pranab, IIT Madras (Jan 2026–)
  5. Mr. Ravi Kalwaniya, IIT Madras (Jan 2023–)
  6. Dr. Surender Kumar, IIT Bhilai (jointly with Dr. Anurag Singh) (August 2021 – December 2024)
  7. Dr. Sumandeep Kaur, Panjab University (jointly with Prof. S.K. Khanduja) (January 2019 - April 2024).


MSc Students.

  1. Mr. Chinmaya Kumar Swain, IIT Madras, 2024-25
  2. Ms. Anjali Maurya, IIT Madras, 2024-25
  3. Ms. Dipti Paik, IIT Madras, 2023-24.
  4. Ms. Ishika Das, IIT Madras, 2023-24.
  5. Mr. Tauqeer Khan, IIT Bhilai, 2021-22.
  6. Ms. Shraddha Bendale, Pt. Ravishankar Shukla University, Raipur, 2021-22.


Project Students.

  1. Mr. Tauqeer Khan, IIT Madras, 2022-2023 (Project Associate in SERB funded project).


Doctoral Committee Member

  1. Mr. Shrinit Singh, Shiv Nadar University (SNU), Greater Noida
  2. Ms. Padmavathy G, IIITDM Kancheepuram
  3. Mr. Arunava Mukhopadhyay, IMSc Chennai
  4. Mr. R. Ganesh Babu, IIT Madras
Research Projects

  1. Project Title : A Study of polynomials over valued fields
    Fund Approved: Rs. 13,67,234/-
    Funding Agency: Start-up Research Grant, DST, Govt. of India.
    Duration: Dec. 2021 - Dec. 2023


  2. Project Title : A study of valued fields and irreducible polynomials
    Fund Approved: Rs. 5,00,000/-
    Funded by: IIT Madras (NFIG)
    Duration: Dec. 2022 - Dec. 2024


  3. Project Title : A study of monogenity of number fields
    Fund Approved: Rs. 26,94,000/-
    Funded by: IIT Madras (NFSG)
    Duration: Nov. 2024 - Nov. 2027

  4. Project Title : Analysis of the coefficients of general $L$-functions and its applications
    Fund Approved: Rs. 30,00,000/-
    Funded by: ANRF ARG-Matrics
    Duration: 2026 - 2030
    Principal Investigator (PI): Dr. Anuj Jakhar

Published/Accepted

  1. A. Jakhar, R Barman, Ravi Kalwaniya, Prabhakar Yadav, Arithmetic Aspects of Number Fields Generated by Polynomial Families,
    J. Pure and Applied Algebra , (2026) accepted.
  2. N. Godara, A. Jakhar, R. Joshi, The generalized ideal counting function along with a weighted kernel function,
    Results in Math. , (2026) accepted.
  3. N. Godara, A. Jakhar, K. Srinivas, Higher Symmetric Powers over arithmetic progressions and applications,
    Quarterly Journal of Mathematics , (2026) accepted.
  4. A. Jakhar, A. Sharma, Power Sums of Symmetric Square Coefficients over Diverse Arithmetic Sequences,
    Quarterly Journal of Mathematics , (2026) accepted.
  5. A. Jakhar, R. Kalwaniya, P. Yadav, A Study of Monogenity of Polynomial Compositions: Qualitative and Quantitative Aspects,
    J. Pure and Applied Algebra , 230 (2026) 108231, 24pp.
  6. N. Godara, A. Jakhar, Quantitative results on sign changes of coefficients of symmetric power $L$-functions,
    Sbornik: Mathematics, accepted (2026).
  7. N. Godara, A. Jakhar, R. Joshi, Generalized divisor problem associated with the number of integral ideals,
    J. Complexity , 95 (2026) 102033, 24pp.
  8. N. Godara, A. Jakhar, R.Joshi, Number Fields with Prescribed p-adic Index,
    The Ramanujan Journal , (2026), accepted.
  9. A. Jakhar, P. Yadav, On Monogenic Polynomials having $k$-full Discriminant,
    Acta Math. Hung. , (2026), accepted.
  10. R. Barman, N. Godara, A. Jakhar, Sums of Coefficients of L-Functions in Residue Classes and Their Applications,
    The Ramanujan Journal , (2026), accepted.
  11. A. Jakhar, M. K. Ram, On Class Groups of Abelian Extensions,
    Canadian Math. Bull. , Published online (2026):1-13. doi:10.4153/S0008439526101775.
  12. A. Jakhar, On Schur's Irreducibility Results and Extended Hermite Polynomials,
    New York J. Math. , 32 (2026) 361-370.
  13. A. Choudhary, A. Jakhar, R.K. Sharma, On the monogenity of composed polynomials,
    Communications in Algebra , (2026), doi:10.1080/00927872.2026.2621258.
  14. A. Jakhar, S. Kotyada, A. Mukhopadhyay, Distinct square-free parts of discriminants of polynomials and quadratic fields,
    The Ramanujan Journal , Vol 69 (2026) Article 38, 12pp. DOI: 10.1007/s11139-026-01314-8.
  15. N. Godara, Anuj Jakhar, Shifted convolution sums and asymptotic analysis of the coefficients of L-function associated with Hecke eigenforms,
    European J. Math. , 12(1) (2026), Paper No. 2, 30pp. accepted.
  16. A. Jakhar, R. Kalwaniya, On the index divisors of certain sextic number fields,
    J. Ramanujan Math. Soc. , 41(1) (2026) 9-14.
  17. Anuj Jakhar, Explicit discriminant and integral basis of $\mathbb{Q}(\sqrt[p^2]{a})$,
    Acta Math. Hung. , (2026), doi: 10.1007/s10474-026-01598-8.
  18. N. Godara, A. Jakhar, S. Kotyada, Asymptotic formula for shifted convolution sums involving the coefficients of an L-function,
    Canad. Math. Bulletin , 69(1) (2026) 236-255.
  19. A. Jakhar, A. Mukhopadhyay, K. Srinivas, On the irreducibility of extended Laguerre polynomials,
    Journal of Algebra and its Applications , (2026) 2650181 (13 pages).
  20. A. Jakhar, S. Kotyada, P. Yadav, Monogenic polynomials having squarefull discriminant,
    Acta Arithmetica , 222 (2026), 99-106.
  21. S. Kaur, A. Jakhar, A note on relative integral basis of number fields defined by $x^n-ax^m-b$,
    Mathematical Notes , 118(3-4) (2025) 744-751.
  22. A. Jakhar, R. Kalwaniya, P. Yadav, A study of monogenity of binomial composition,
    Acta Arithmetica , 221 (2025), 387-395.
  23. N. Godara, A. Jakhar, R. Joshi, Constructing infinite families of number fields with fixed indices via sextinomials,
    Math. Slovaca , (2025), doi:10.1515/ms-2026-0137.
  24. Anuj Jakhar, K. Srinivas, and A. Mukhopadhyay, Squarefree part of a discriminant and abc-conjecture,
    Proc. of Lie Algebra and Number Theory , Springer, (2025) accepted.
  25. A. Jakhar, A. Mukhopadhyay, K. Srinivas, Distinct Squarefree Parts of Discriminants of some Polynomials and Quadratic Fields,
    Results in Mathematics , 80(5) (2025) Paper No. 132, 9pp. DOI: 10.1007/s00025-025-02448-9.
  26. A. Jakhar, A. Mukhopadhyay, K. Srinivas, Monogenic polynomials and symmetric Galois groups: a quantitative study,
    The Ramanujan Journal , Vol 67 (2025) Article 69. DOI: 10.1007/s11139-025-01110-w.
  27. A. Jakhar, R. Kalwaniya, K. Srinivas, On monogenity of number fields and Galois group,
    Int. J. Number Theory , 21(8) (2025) 1995-2013. doi: 10.1142/S1793042125500964.
  28. A. Jakhar, S. Laishram, P. Yadav, Explicit discriminant of a class of polymoial, Monogenity and Galois group,
    Commun. Algebra , 53(7) (2025), 2937-2948.
  29. A. Jakhar, Nonmonogenity of number fields defined by exponential Taylor polynomials,
    Bull. Aust. Math. Soc. , 111 (2025), 497-504. DOI: 10.1017/S0004972724000819.
  30. A. Jakhar, R. Kalwaniya, An extension of a second irreducibility theorem of I. Schur,
    Acta Mathematica Hung. , 174 (2024), 289-298. DOI: 10.1007/s10474-024-01478-z.
  31. A. Jakhar, R. Kalwaniya, P. Yadav, On the monogenity and Galois group of certain classes of polynomials,
    Math. Slovaca , 74(5) (2024), 1147-1154. DOI: 10.1515/ms-2024-0082.
  32. Anuj Jakhar, Characterisation of primes dividing the index of a class of polynomials and its applications,
    Bull. Aust. Math. Soc. , 110 (2024) 460-467, DOI:10.1017/S0004972724000182.
  33. Anuj Jakhar, N. Sangwan, Explicit discriminant and integral basis of pure nonic fields,
    Journal of Ramanujan Math. Soc. , 39 (3) (2024) 293-305.
  34. Anuj Jakhar, On the irreducible factors of a polynomial over a valued field,
    Czech. Math. Journal , 74 (2024) 367-375, DOI:10.21136/CMJ.2024.0451-22.
  35. Anuj Jakhar, S. Kumar, Non-monogenity of some number fields generated by binomials or trinomials of prime-power degree,
    Journal of Algebra and its Applications , (2024), 2450095 (8 pages). DOI: 10.1142/S0219498824500956.
  36. Anuj Jakhar, S. Kumar, S. Kaur, On Non-monogenity of the number fields defined by certain quadrinomials,
    Communications in Algebra , (2023), 51(6), 2448-2459, DOI:10.1080/00927872.2022.2162913.
  37. Anuj Jakhar, N. Sangwan, Irreducibility criteria for factorial modules,
    Communications in Algebra , 51(5) (2023) 1826-1829, DOI:10.1080/00927872.2022.2145295.
  38. Anuj Jakhar, On non-monogenic algebraic number fields,
    Rocky Mountain J. Math. , 53(1) (2023), 103-110. DOI: 10.1216/rmj.2023.53.103.
  39. Anuj Jakhar, S. Kaur, S.K. Khanduja, Discriminant and integral basis of quintic fields defined by $x^5+ax+b$,
    Journal of Algebra and its Applications , (2023), 2350109 (37 pages), DOI: 10.1142/S0219498823501098.
  40. Anuj Jakhar, S. Kaur, A note on non-monogenity of number fields arised from sextic trinomials,
    Quaestiones Mathematicae , 46(5) (2023) 833-840, DOI:10.2989/16073606.2022.2043948.
  41. Anuj Jakhar, S. Kaur, S. Kumar, On power basis of a class of number fields,
    Mediterranean Journal of Mathematics , 20(6)(2023) 315, 11pp; DOI: 10.1007/s00009-023-02522-y.
  42. Anuj Jakhar, S. Kaur, S. Kumar, On monogenity of certain octic number fields,
    Colloquium Mathematicum , 171(1) (2023) 145-152, DOI: 10.4064/cm8799-3-2022.
  43. Anuj Jakhar, S. Kaur, S. Kumar, Common index divisor of the number fields defined by x^5+ax+b,
    Proceedings of the Edinburgh Mathematical Society , 65(4) (2022) 1147-1161, DOI:10.1017/S0013091522000529.
  44. Anuj Jakhar, Explicit integral basis of Q(\sqrt[p_1p_2]{a}),
    Journal of Number Theory , 240 (2022) 254-271. DOI: 10.1016/j.jnt.2022.01.009.
  45. Anuj Jakhar, Nonmonogenity of number fields defined by trinomials,
    New York Journal of Mathematics , 28 (2022) 650-658.
  46. Anuj Jakhar, K. Srinivas, On the degrees of irreducible factors of a polynomial,
    Proceedings of American Mathematical Society , 150(5) (2022) 1949-1953. DOI:10.1090/proc/15918.
  47. Anuj Jakhar, S. Kumar, On non-monogenic number fields defined by sextic trinomials,
    Canadian Math. Bulletin , 65(3) (2022) 788-794, DOI:10.4153/S0008439521000825.
  48. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On discriminant of pure number fields,
    Colloquium Mathematicum , 167 (2022) 149-157. DOI:10.4064/cm8257-11-2020.
  49. Anuj Jakhar, A simple generalization of the Schönemann-Eisenstein irreducibility criterion,
    Archiv der Mathematik , 117(4) (2021) 375-378. DOI: 10.1007/s00013-021-01642-9.
  50. Anuj Jakhar, N. Sangwan, Key polynomials and distinguished pairs,
    Communications in Algebra , 49(7) (2021) 2952-2960, DOI:10.1080/00927872.2021.1885679.
  51. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On integral basis of pure number fields,
    Mathematika , 67 (2021) 187-195. DOI:10.1112/mtk.12067.
  52. Anuj Jakhar, Explicit integral basis of pure sextic number fields,
    Rocky Mountain Journal of Math. , 51(2) (2021) 571-580. DOI: 10.1216/rmj.2021.51.571.
  53. Anuj Jakhar, S. K. Khanduja, A note on Dedekind criterion,
    Journal of Algebra and its applications , (2021) 2150066 (7 pages). DOI:10.1142/S0219498821500663.
  54. Anuj Jakhar, On primes dividing the index of a quadrinomial,
    Rocky Mountain Journal of Math. , 50(6) (2020) 2117-2125. DOI: 10.1216/rmj.2020.50.2117.
  55. Anuj Jakhar, K. Srinivas, On the irreducible factors of a polynomial II,
    Journal of Algebra , 556 (2020) 649-655. DOI:10.1016/j.jalgebra.2020.02.045.
  56. Anuj Jakhar, On the irreducible factors of a polynomial,
    Proceedings of American Mathematical Society , 148 (2020) 1429-1437. DOI:10.1090/proc/14856.
  57. Anuj Jakhar, On the factors of a polynomial,
    Bulletin of London Mathematical Society , 52 (2020) 158-160. DOI:10.1112/blms.12315.
  58. Anuj Jakhar, S. K. Khanduja, On the index of an algebraic integer and beyond,
    Journal of Pure and Applied Algebra , 224 (2020) 106281. DOI:10.1016/j.jpaa.2019.106281.
  59. A. Jakhar, S.K. Khanduja, N. Sangwan, Corrigendum to On prolongations of valuations to the composite field,
    Journal of Pure and Applied Algebra , 224(10) (2020) 106397.
  60. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On prolongations of a valuation to the composite field,
    Journal of Pure and Applied Algebra , 224(2) (2020) 551-558. DOI: 10.1016/j.jpaa.2019.05.021.
  61. Anuj Jakhar, S. K. Khanduja, N. Sangwan, Some Results on Integrally Closed Domains,
    Contemporary Math., American Mathematical Society , 738 (2019) 75-80. DOI: 10.1090/conm/738.
  62. Anuj Jakhar, A Useful Irreducibility Test for Integer Polynomials,
    American Math. Monthly , 126(10) (2019) 943-944. DOI:10.1080/00029890.2019.1655334.
  63. Anuj Jakhar, N. Sangwan, Integral basis of pure prime degree number fields,
    Indian Journal of Pure and Applied Mathematics , 50(2) (2019) 309-314. DOI:10.1007/s13226-019-0326-7.
  64. Anuj Jakhar, N. Sangwan, Some results for the irreducibility of truncated binomial expansions,
    Journal of Number Theory , 192 (2018) 143-149. DOI:10.1016/j.jnt.2018.04.001.
  65. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On the compositum of integral closures of valuation rings,
    Journal of Pure and Applied Algebra , 222(11) (2018) 3560-3565. DOI:10.1016/j.jpaa.2017.12.023.
  66. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On factorization of polynomials over henselian valued fields,
    Communications in Algebra , 46(7) (2018) 3205-3221. DOI:10.1080/00927872.2017.1407423.
  67. Anuj Jakhar, An Irreducibility Criterion for Polynomials with Integer Coefficients,
    American Math. Monthly , 125(5) (2018) 464-465. DOI:10.1080/00029890.2018.1436841.
  68. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On integrally closed simple extensions of valuation rings,
    Journal of Pure and Applied Algebra , 222 (2018) 889-899. DOI:10.1016/j.jpaa.2017.05.012.
  69. Anuj Jakhar, On a mild generalization of the Schönemann - Eisenstein - Dumas Irreducibility Criterion,
    Communications in Algebra , 46 (1) (2018) 114-118. DOI:10.1080/00927872.2017.1313424.
  70. Anuj Jakhar, S. K. Khanduja, N. Sangwan, Characterization of primes dividing the index of a trinomial,
    International Journal of Number Theory , 13, No. 10 (2017) 2505-2514. DOI:10.1142/S1793042117501391.
  71. Anuj Jakhar, S. K. Khanduja, N. Sangwan, Discriminant of pure squarefree degree number fields,
    Acta Arithmetica , 181 (2017) 287-296. DOI:10.4064/aa170508-4-11.
  72. Anuj Jakhar, N. Sangwan, On a mild generalization of the Schönemann Irreducibility criterion,
    Communications in Algebra , 45 (4) (2017) 1757-1759. DOI:10.1080/00927872.2016.1226320.
  73. Anuj Jakhar, B. Jhorar, S. K. Khanduja, N. Sangwan, Discriminant as a product of local discriminants,
    Journal of Algebra and its applications , 16 (2) (2017) (7 pages). DOI:10.1142/S0219498817501985.
  74. Anuj Jakhar, A note on the irreducibility of polynomials,
    The Math. Student , 86 (3-4) (2017), 51-53.
  75. Anuj Jakhar, N. Sangwan, An irreducibility criterion for integer polynomials,
    The Math. Student , 85 (3-4) (2016) 63-66.
  76. Anuj Jakhar, S. K. Khanduja, N. Sangwan, On prime divisors of the index of an algebraic integer,
    Journal of Number Theory , 166 (2016) 47-61. DOI:10.1016/j.jnt.2016.02.021.



  1. A. Jakhar, R Barman, Ravi Kalwaniya, Prabhakar Yadav, Arithmetic Aspects of Number Fields Generated by Polynomial Families,
    J. Pure and Applied Algebra , (2026) accepted.
  2. N. Godara, A. Jakhar, K. Srinivas, Higher Symmetric Powers over arithmetic progressions and applications,
    Quarterly Journal of Mathematics , (2026) accepted.
  3. A. Jakhar, A. Sharma, Power Sums of Symmetric Square Coefficients over Diverse Arithmetic Sequences,
    Quarterly Journal of Mathematics , (2026) accepted.
  4. A. Jakhar, R. Kalwaniya, P. Yadav, A Study of Monogenity of Polynomial Compositions: Qualitative and Quantitative Aspects,
    J. Pure and Applied Algebra , 230 (2026) 108231, 24pp.
  5. N. Godara, A. Jakhar, R. Joshi, Generalized divisor problem associated with the number of integral ideals,
    J. Complexity , 95 (2026) 102033, 24pp.
  6. N. Godara, A. Jakhar, K. Srinivas, Asymptotic formula for shifted convolution sums involving the coefficients of an L-function
    Canadian Math. Bull. (2025), DOI: 10.4153/S0008439525100854.
  7. A. Jakhar, On Schur's Irreducibility Results and Extended Hermite Polynomials,
    New York J. Math. , 32 (2026) 361-370.
  8. A. Jakhar, A. Mukhopadhyay, K. Srinivas, Monogenic polynomials and symmetric Galois groups: a quantitative study,
    The Ramanujan Journal, Vol 67 (2025) Article 69.
  9. Anuj Jakhar, S. Kaur, S. Kumar, Common index divisor of the number fields defined by x^5+ax+b,
    Proceedings of the Edinburgh Mathematical Society (2022), 65(4) 1147 - 1161.
  10. A. Jakhar, Nonmonogenity of number fields defined by trinomials,
    New York Journal of Mathematics 28 (2022) 650-658.
  11. A. Jakhar, Explicit integral basis of Q(a^{p_1p_2}),
    Journal of Number Theory 240 (2022) 254-271. DOI: 10.1016/j.jnt.2022.01.009.
  12. A. Jakhar, K. Srinivas, On the degrees of irreducible factors of a polynomial,
    Proc. Amer. Math. Soc. 150(5) (2022), 1949-1953. DOI:10.1090/proc/15918.
  13. A. Jakhar, A simple generalization of the Schonemann-Eisenstein irreducibility criterion
    Archiv der Mathematik 117(4) (2021) 375-378.
  14. A. Jakhar, S.K. Khanduja, N. Sangwan, On Integral basis of pure number fields,
    Mathematika 67 (2021) 187–195.
  15. A. Jakhar, K. Srinivas, On the irreducible factors of a polynomial II,
    Journal of Algebra 556 (2020) 649-655.
  16. A. Jakhar, On the irreducible factors of a polynomial,
    Proceedings of American Mathematical Society 148 (2020) 1429-1437.
  17. A. Jakhar, On the factors of a polynomial,
    Bulletin of London Mathematical Society 52 (2020) 158-160.
  18. A. Jakhar, S.K. Khanduja, On the index of an algebraic integer and beyond,
    Journal of Pure and Applied Algebra 224 (2020) 106281.
  19. A. Jakhar, S.K. Khanduja, N. Sangwan, On prolongations of valuations to the composite field,
    Journal of Pure and Applied Algebra 224(2) (2020) 551-558.
  20. A. Jakhar, S.K. Khanduja, N. Sangwan, On the compositum of integral closures of valuation rings,
    Journal of Pure and Applied Algebra 222(11) (2018) 3560-3565.
  21. A. Jakhar, N. Sangwan, Some results for the irreducibility of truncated binomial expansions,
    Journal of Number Theory 192 (2018) 143–149.
  22. A. Jakhar, S.K. Khanduja, N. Sangwan, On integrally closed simple extensions of valuation rings,
    Journal of Pure and Applied Algebra 222 (2018) 889-899.
  23. A. Jakhar, S.K. Khanduja, N. Sangwan, On prime divisors of the index of an algebraic integer,
    Journal of Number Theory 166 (2016) 47–61.