Anuj Jakhar
Assistant Professor
Department of Mathematics
Indian Institute of Technology Madras
Ph.D. Students

  1. Ms. Sumita Gunri, IIT Madras (2024–)
  2. Mr. Ravi Kalwaniya, IIT Madras (2023–)
  3. Mr. Surender Kumar, IIT Bhilai (jointly with Dr. Anurag Singh) (2021–thesis submitted in June 2024)
  4. 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

Published/Accepted

  1. A. Jakhar, Nonmonogenity of number fields defined by exponential Taylor polynomials,
    Bull. Aust. Math. Soc. (2024), to appear.
  2. A. Jakhar, R. Kalwaniya, An extension of a second irreducibility theorem of I. Schur,
    Acta Mathematica Hung. (2024), to appear.
  3. A. Jakhar, R. Kalwaniya, P. Yadav,On the monogenity and Galois group of certain classes of polynomials,
    Math. Slovaca (2024), to appear.
  4. Anuj Jakhar, Characterisation of primes dividing the index of a class of polynomials and its applications,
    Bull. Aust. Math. Soc. (2024), DOI:10.1017/S0004972724000182.
  5. Anuj Jakhar, On the irreducible factors of a polynomial over a valued field,
    Czech Math. Journal (2024), accepted.
  6. Anuj Jakhar, N. Sangwan, Explicit discriminant and integral basis of pure nonic fields,
    Journal of Ramanujan Math. Soc. (2023), accepted.
  7. Anuj Jakhar, S. Kaur, S. Kamar, On power basis of a class of number fields,
    Mediterranean Journal of Mathematics (2023), DOI: 10.1007/s00009-023-02522-y.
  8. 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.
  9. 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 (2022), DOI:10.1142/S0219498824500956.
  10. 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.
  11. A. Jakhar, N. Sangwan, Irreducibility criteria for factorial modules,
    Communications in Algebra (2023), 51(5) 1826-1829.
  12. A. Jakhar, On non-monogenic algebraic number fields,
    Rocky Mountain J. Math. (2022), accepted.
  13. A. Jakhar, Nonmonogenity of number fields defined by trinomials,
    New York Journal of Mathematics 28 (2022) 650-658.
  14. A. Jakhar, S. Kaur, S. Kumar, On monogenity of certain octic number fields,
    Colloq. Math. 171(1) (2023), 145-152. DOI: 10.4064/cm8799-3-2022.
  15. 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.
  16. A. Jakhar, S. Kaur, A note on non-monogenity of number fields arised from sextic trinomials,
    Quaestiones Mathematicae 46 (2023) 833-840, DOI:10.2989/16073606.2022.2043948.
  17. A. Jakhar, S. Kaur, S.K. Khanduja, Discriminant and integral basis of quintic fields defined by x5+ax+b,
    Journal of Algebra and its Applications (2023), 2350109 (37 pages), DOI: 10.1142/S0219498823501098.
  18. 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.
  19. A. Jakhar, S. Kumar, On non-monogenic number fields defined by sextic trinomials,
    Canadian Math. Bulletin (2022), DOI: 10.4153/S0008439521000825.
  20. A. Jakhar, A simple generalization of the Schonemann-Eisenstein irreducibility criterion
    Archiv der Mathematik 117(4) (2021) 375-378.
  21. A. Jakhar, N. Sangwan, Key polynomials and distinguished pairs,
    Communications in Algebra 49(7) (2021) 2952-2960.
  22. A. Jakhar, S.K. Khanduja, N. Sangwan, On discriminant of pure number fields,
    Colloq. Math. 167 (2022), 149-157. DOI:10.4064/cm8257-11-2020.
  23. A. Jakhar, Explicit integral basis of pure sextic number fields,
    Rocky Mountain J. Math. 51(2) (2021) 571-580.
  24. A. Jakhar, S.K. Khanduja, N. Sangwan, On Integral basis of pure number fields,
    Mathematika 67 (2021) 187–195.
  25. A. Jakhar, S.K. Khanduja, A note on Dedekind criterion,
    Journal of Algebra and its applications (2021) 2150066 (7 pages).
  26. A. Jakhar, On primes dividing the index of a quadrinomial,
    Rocky Mountain J. Math. 50(6) (2020) 2117-2125.
  27. A. Jakhar, K. Srinivas, On the irreducible factors of a polynomial II,
    Journal of Algebra 556 (2020) 649-655.
  28. A. Jakhar, On the irreducible factors of a polynomial,
    Proceedings of American Mathematical Society 148 (2020) 1429-1437.
  29. A. Jakhar, On the factors of a polynomial,
    Bulletin of London Mathematical Society 52 (2020) 158-160.
  30. A. Jakhar, S.K. Khanduja, On the index of an algebraic integer and beyond,
    Journal of Pure and Applied Algebra 224 (2020) 106281.
  31. 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.
  32. 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.
  33. A. Jakhar, A Useful Irreducibility Test for Integer Polynomials,
    American Math. Monthly 126(10) (2019) 943-944.
  34. A. Jakhar, S.K. Khanduja, N. Sangwan, Some Results on Integrally Closed Domains,
    Contemporary Mathematics, Amer. Math. Soc. 738 (2019) 75-80.
  35. A. Jakhar, N. Sangwan, Integral basis of pure prime degree number fields,
    Indian Journal of Pure and Applied Mathematics 50(2) (2019) 309-314.
  36. 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.
  37. A. Jakhar, S.K. Khanduja, N. Sangwan, On factorization of polynomials over henselian valued fields,
    Communications in Algebra 46(7) (2018) 3205-3221.
  38. A. Jakhar, N. Sangwan, Some results for the irreducibility of truncated binomial expansions,
    Journal of Number Theory 192 (2018) 143–149.
  39. A. Jakhar, An Irreducibility Criterion for Polynomials with Integer Coefficients,
    American Math. Monthly 125(5) (2018) 464-465.
  40. 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.
  41. A. Jakhar, On a mild generalization of the Schönemann - Eisenstein - Dumas Irreducibility Criterion,
    Communications in Algebra 46 (1) (2018) 114–118.
  42. A. 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.
  43. A. Jakhar, S.K. Khanduja, N. Sangwan, Discriminant of pure squarefree degree number fields,
    Acta Arithmetica 181 (2017) 287-296.
  44. A. Jakhar, A note on the irreducibility of polynomials,
    The Math. Student 86 (3-4) (2017) 51-53.
  45. A. Jakhar, N. Sangwan, On a mild generalization of the Schönemann Irreducibility criterion,
    Communications in Algebra 45 (4) (2017) 1757–1759.
  46. A. 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).
  47. A. Jakhar, N. Sangwan, An irreducibility criterion for integer polynomials,
    The Math. Student 85 (3-4) (2016) 63-66.
  48. 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.


Submitted/Preprint.

  1. A. Jakhar, R. Kalwaniya, K. Srinivas, On monogenity of number fields and Galois group, 2024, submitted.
  2. A. Jakhar, S. Laishram, P. Yadav, Explicit discriminant of a class of polymoial, Monogenity and Galois group, 2024, submitted.
  3. A. Jakhar, R. Kalwaniya, P. Yadav, A study of monogenity of Binomial Composition, 2024, submitted
  4. A. Jakhar, R. Kalwaniya, P. Yadav, On the monogenity and Galois group of certain classes of polynomials, 2024, submitted
  5. A. Jakhar, S. Kumar, Discriminant and integral basis of Q(a^{1/12}), 2024, arXiv:2304.00339.
  6. A. Jakhar, R. Kalwaniya, On the index divisors of certain number fields, 2023, arXiv:2303.00484.
  7. A. Jakhar, On Schur’s irreducibility results and generalised φ-Hermite polynomials, 2023, submitted.
  8. A. Jakhar, R. Kalwaniya, An extension of a second irreducibility theorem of I. Schur, 2023, submitted.
  9. A. Jakhar, A. Mukhopadhyay, K. Srinivas, On the irreducibility of extended Laguerre Polynomials, 2023, submitted.
  10. A. Jakhar, K. Srinivas, A short note on number fields defined by exponential Taylor polynomials, submitted, 2023.
  11. A. Jakhar, N. Sangwan, Explicit discriminant of Kummer extensions having degree $p^2$, under preparation (2024).

  1. 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.
  2. A. Jakhar, Nonmonogenity of number fields defined by trinomials,
    New York Journal of Mathematics 28 (2022) 650-658.
  3. 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.
  4. 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.
  5. A. Jakhar, A simple generalization of the Schonemann-Eisenstein irreducibility criterion
    Archiv der Mathematik 117(4) (2021) 375-378.
  6. A. Jakhar, S.K. Khanduja, N. Sangwan, On Integral basis of pure number fields,
    Mathematika 67 (2021) 187–195.
  7. A. Jakhar, K. Srinivas, On the irreducible factors of a polynomial II,
    Journal of Algebra 556 (2020) 649-655.
  8. A. Jakhar, On the irreducible factors of a polynomial,
    Proceedings of American Mathematical Society 148 (2020) 1429-1437.
  9. A. Jakhar, On the factors of a polynomial,
    Bulletin of London Mathematical Society 52 (2020) 158-160.
  10. A. Jakhar, S.K. Khanduja, On the index of an algebraic integer and beyond,
    Journal of Pure and Applied Algebra 224 (2020) 106281.
  11. 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.
  12. 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.
  13. A. Jakhar, N. Sangwan, Some results for the irreducibility of truncated binomial expansions,
    Journal of Number Theory 192 (2018) 143–149.
  14. 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.
  15. 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.


Address : NAC-548, Department of Mathematics , IIT Madras, Chennai, PO 600113.
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