Prof. S. A. Katre
Department of Mathematics
University of Pune
Pune 411 007, INDIA
e-mail: sakatre at math dot unipune dot ernet dot in
e-mail: sakatre at bprim dot org
Phone :(Off.) 91-020-5696061 ext. 2112   (Res.)91-020-64001328
Acting Director of Bhaskaracharaya Pratishthan (Hon.)

Ph. D. 1985 Panjab University, India.
Thesis adviser: A. R. Rajwade.
Thesis: Complete Solution of the Cyclotomic Problem for a Prime Modulus and Related Topics.
1988-up-to-date : University of Pune, Pune. Current Position : Professor
Specialization : Number Theory
Other Topics of Interest : Algebra, Combinatorics

Visits/Conferences Abroad

1. Mar del Plata, Argentina - Worked as Deputy Leader of the Indian Team in the International Mathematical Olympiad (IMO-97).
2. International Congress of Mathematicians (ICM-98) Berlin, Germany, 18th-27th Aug. 1998   - Presented a paper.
3. One Month Visit to Institut de Mathematique de Luminy, Marseille, France (8 Oct. - 6 Nov. 1999).   - Participated in the International Conference on Arithmetic, Geometry and Coding Theory (AGCT-7)(25th-29th Oct. 1999) and presented a paper.
4. International Congress of Mathematicians (ICM-2002) China.

List of publications of Prof. S. A. Katre


Ph.D. Thesis

Complete Solution of the Cyclotomic Problem for a Prime Modulus and Related Topics, Panjab Univ. (1984) - Supervisor : A. R. Rajwade.

Research Papers

  1. On the Jacobsthal sum f+9(a) and the related sum y+9(a), Math. Scand. 53 (1983), 193-202 (with A. R. Rajwade).    MR 86c:11061
  2. Jacobsthal sums in terms of quadratic partitions of a prime, Proc. Conference in Number Theory, Ootacamund, India, 1984, Lecture Notes in Math., Springer Verlag 1122 (1985), 153-162.    MR 87b:11081/li>
  3. Euler’s criterion for quintic nonresidues, Canadian J. Math. 37 (1985), 1008-1024 (with A. R. Rajwade).    MR 87c:11020
  4. Unique determination of cyclotomic numbers of order five, Manuscripta Math. 53 (1985), 65-75 (with A. R. Rajwade).    MR 86k:11020
  5. Complete solution of the cyclotomic problem in Fq for any prime modulus l,q = pa+,p =_ 1 (mod l), Acta Arith. 45 (1985), 183-199 (with A. R. Rajwade).    MR 87d:11095
  6. On the Jacobsthal sum f+4(a) and the related sum y+8(a), Ann. Univ. Sci. Budapest Eotvos Sect. Math. 29 (1986), 3-7 (with A. R. Rajwade).     MR 88m:11066
  7. Jacobsthal sums of prime order, Indian J. Pure Appl. Math. 17 (1986), 1345-1362 (with A. R. Rajwade).    MR 88a:11132
  8. Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum, Math. Scand. 60 (1987), 52-62 (with A. R. Rajwade). MR 88j:11047
  9. Cyclotomic numbers and a conjecture of Snapper, Indian J. Pure Appl. Math. 20 (1989), 99-103.    MR 90e:11185
  10. A discriminant criterion for matrices over orders in algebraic number fields to be sums of squares, Proc. Symp. on Algebra and Number Th., Kochi, Kerala (1990), 31-38 (with Sangita A. Khule). MR 92m:11125
  11. numbers of order 2l,l an odd prime, Acta Arith. 69 (1995), 51-74 (with V. V. Acharya).    MR 95j:11115
  12. > Explicit evaluation of cyclotomic numbers of prime order, A. V. Prasad Memorial Volume of Ranchi Univ. Mathematical Journal 28 (1997), 77-84 (with Anuradha Narasimhan). MR 2000b:11135
  13. Number of points on the projective curves aY l = bXl + cZl and aY 2l = bX2l +cZ2l defined over finite fields, l an odd prime, J. Number Th. 77 No. 2 (1999), 288-313 (with N. Anuradha) MR 2000h:11067
  14. Matrices over orders in algebraic number fields as sums of k-th powers, Proc. Amer. Math. Soc. 128(3)(March, 2000), 671-675 (with Sangita A. Khule).    MR 2000e:11026
  15. Twin prime conjecture and generalisations, Bulletin of the Marathwada Math. Soc., 2( 2001), 64-70
  16. Jacobsthal sums of order 6 (preprint) (with V. V. Acharya)

Articles Published in Proceedings and Pedagogical Journals

1. On numbers of solutions of equations over finite fields, Proc. Instructional School, Alg. Nr. Th., Mumbai Univ. (1995), 7pp.
2. The Logo for IMO-1996, Bona Mathematica Vol.7, No.1-2 (1996), 3-5.
3. How to factorise x100 -1, Bona Mathematica Vol.8, No.2 (1997), 33-41.
4. Gauss-Jacobi sums and Stickelberger theorem, in Cyclotomic Fields and Related Topics, Proc. Summer School, 1999, Pune, Eds. S. D. Ad- hikari, S. A. Katre and Dinesh Thakur, Bhaskaracharya Pratishthana, Pune (2000), 75-92.
5. The cyclotomic problem, in Current Trends in Number Theory, Proc. International Conf. on Number Theory, 2000, HRI, Allahabad, Eds. S. D. Adhikari, S. A. Katre and B. Ramakrishnan, Hindustan Book Agency, New Delhi (2002).

Books Edited:

1. An Excursion in Mathematics (4rd Edition), published by Regional Coordinator, RMO and INMO, Bhaskaracharya Pratishthana, Pune, 2000 (with M. R. Modak and V. V. Acharya).
2. Topics in Discrete Mathematics : Codes, Tableaux, Designs and Graphs, Proceedings of All India Winter School in Discrete Mathematics, Dept. of Mathematics, Univ. of Pune-1989, New Age International Publications, 1997 (with N. M. Singhi, N. S. Gopala Krishnan and D. M. Kulkarni).
3. Cyclotomic Fields and Related Topics, Proceedings of “Summer School on Cyclotomic Fields, 1999”, Bhaskaracharya Pratishthana, Pune, 2000 (with S. D. Adhikari and Dinesh Thakur) MR 2001f:11004
4. Current Trends in Number Theory, Proceedings of the HRI Interna- tional Conference on Number Theory, 2000, published by Hindusthan Book Agency, New Delhi, 2002 (with S. D. Adhikari and B. Ramakr- ishnan).

Journals Edited:

1. Bona Mathematica (A Pedagogical Journal in Mathematics): Chief Editor - 1995 onwards.
Working on the editorial board of the following Indian journals:
1. Ranchi Univ. Mathematical Journal
2. Bulletin of the Marathwada Mathematical Society