# zbMATH — the first resource for mathematics

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 Documents Indexed: 51 Publications since 1968, including 3 Books Reviewing Activity: 68 Reviews
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#### Co-Authors

 20 single-authored 18 Parnami, J. C. 8 Katre, Shashikant A. 3 Pall, Satinder 3 Rishi, Dharam Bir 1 Nashier, Budh Singh 1 Singh, Surjit
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#### Serials

 7 Indian Journal of Pure & Applied Mathematics 6 Proceedings of the Cambridge Philosophical Society 4 Acta Arithmetica 4 Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica 4 The Mathematics Student 3 The Journal of the Indian Mathematical Society. New Series 3 L’Enseignement Mathématique. 2e Série 2 Journal of Number Theory 2 Mathematica Scandinavica 2 Bulletin de la Société Matheḿatique de Belgique. Série B 2 Texts and Readings in Mathematics 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Canadian Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Pacific Journal of Mathematics 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Rendiconti del Seminario Matematico 1 Journal of the Australian Mathematical Society. Series A 1 Bulletin de la Société Mathématique de Belgique. Série A 1 London Mathematical Society Lecture Note Series
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#### Fields

 44 Number theory (11-XX) 8 Algebraic geometry (14-XX) 4 Field theory and polynomials (12-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Convex and discrete geometry (52-XX)

#### Citations contained in zbMATH Open

36 Publications have been cited 125 times in 66 Documents Cited by Year
Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum. Zbl 0602.12005
Katre, S. A.; Rajwade, A. R.
1987
The Diophantine equation $$y^2=x(x^2+21\,Dx+112\,D^2)$$ and the conjectures of Birch and Swinnerton-Dyer. Zbl 0382.14006
1977
Complete solution of the cyclotomic problem in $$\mathbb F_q$$ for any prime modulus $$\ell$$, $$q=p^{\alpha}$$, $$p\equiv 1\pmod \ell$$. Zbl 0525.12015
Katre, S. A.; Rajwade, A. R.
1985
Squares. Zbl 0785.11022
1993
Jacobi sums and cyclotomic numbers for a finite field. Zbl 0491.12019
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1982
Arithmetic on corves with complex multiplication by $$\sqrt{-2}$$. Zbl 0188.25001
1968
Certain classical congruences via elliptic curves. Zbl 0277.10028
1974
A new cubic character sum. Zbl 0488.10036
Rajwade, A. R.; Parnami, J. C.
1982
On rational primes p congruent to 1 (mod 3 or 5). Zbl 0182.07603
1969
Unique determination of cyclotomic numbers of order five. Zbl 0577.12014
Katre, S. A.; Rajwade, A. R.
1985
Arithmetic on curves with complex multiplication by the Eisenstein integers. Zbl 0165.54804
1969
The number of solutions of the congruence $$y^2 \equiv x^4 - a (mod \;p)$$. Zbl 0298.10016
1974
A note on the number of solutions $$N_ p$$ of the congruence $$y^ 2\equiv x^ 3-Dx (\mod p)$$. Zbl 0194.07901
1970
Evaluation of a cubic character sum using the $$\sqrt{-19}$$ division points of the curve $$y^ 2=x^ 3-2^ 3\cdot 19x+2\cdot 19^ 2$$. Zbl 0547.10033
Rishi, Dharam Bir; Parnami, J. C.; Rajwade, A. R.
1984
A note on the stufe of quadratic fields. Zbl 0363.12003
1975
Determination of a unique solution of the quadratic partition for primes $$p\equiv 1 (\mod 7)$$. Zbl 0366.10002
Nashier, Budh Singh; Rajwade, A. R.
1977
On the congruence $$y^2 \equiv x^5 - a\pmod p$$. Zbl 0272.12001
1973
Surprises and counterexamples in real function theory. Zbl 1126.26002
Rajwade, A. R.; Bhandari, A. K.
2007
Jacobsthal sums of prime order. Zbl 0605.10020
Katre, S. A.; Rajwade, A. R.
1986
Criterion for 2 to be an $$\ell$$th power. Zbl 0539.10006
Parnami, J. C.; Agrawal, M. K.; Pall, Satinder; Rajwade, A. R.
1984
Euler’s criterion for quintic nonresidues. Zbl 0564.10003
Katre, S. A.; Rajwade, A. R.
1985
The period equation for primes $$p$$ congruent to $$1 (mod 5)$$. Zbl 0206.34601
1971
Notes on the congruence $$y^2\equiv x^5-a\;(\mod p)$$. Zbl 0306.10004
1975
Some formulae for elliptic curves with complex multiplication. Zbl 0375.14011
1977
The number of solutions of the congruence $$y^2 \equiv x^6-a\pmod p$$. Zbl 0265.10002
1973
Some congruences in algebraic integers and rational integers. Zbl 0405.10004
1976
On some trigonometric diophantine equations of the type $$\sqrt{n} = c_ 1 \cos \pi d_ 1 +\dots + c_\lambda \cos \pi d_\lambda$$. Zbl 0474.10018
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1981
A congruence relation between the coefficients of the Jacobi sum. Zbl 0483.12004
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1981
On the 4-power stufe of a field. Zbl 0493.10032
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1981
On expressing $$\sqrt{p}$$ as a rational linear combination of cosines of angles which are rational multiples of $$\pi$$. Zbl 0501.10016
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1982
On expressing a quadratic irrational as a rational linear combination of roots of unity. Zbl 0501.10017
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1982
On the Jacobsthal sum $$\Phi_ 9(a)$$ and the related sum $$\psi_ 9(a)$$. Zbl 0512.10031
Katre, S. A.; Rajwade, A. R.
1983
Power stufe of Galois fields. Zbl 0603.12009
1983
Triangles and cyclic quadrilaterals, with angles that are rational multiples of $$\pi$$ and sides at most quadratic over the rationals. Zbl 0709.11010
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1987
The number of points on the curve $$y^2=x^5+a$$ in $$\mathbb F_q$$ and application to local $$\zeta$$-function. Zbl 0556.14013
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1984
Complex multipliction by $$(1+\sqrt{-19})/2$$. Zbl 0559.14029
Rishi, Dharam Bir; Parnami, J. C.; Rajwade, A. R.
1983
Surprises and counterexamples in real function theory. Zbl 1126.26002
Rajwade, A. R.; Bhandari, A. K.
2007
Squares. Zbl 0785.11022
1993
Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum. Zbl 0602.12005
Katre, S. A.; Rajwade, A. R.
1987
Triangles and cyclic quadrilaterals, with angles that are rational multiples of $$\pi$$ and sides at most quadratic over the rationals. Zbl 0709.11010
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1987
Jacobsthal sums of prime order. Zbl 0605.10020
Katre, S. A.; Rajwade, A. R.
1986
Complete solution of the cyclotomic problem in $$\mathbb F_q$$ for any prime modulus $$\ell$$, $$q=p^{\alpha}$$, $$p\equiv 1\pmod \ell$$. Zbl 0525.12015
Katre, S. A.; Rajwade, A. R.
1985
Unique determination of cyclotomic numbers of order five. Zbl 0577.12014
Katre, S. A.; Rajwade, A. R.
1985
Euler’s criterion for quintic nonresidues. Zbl 0564.10003
Katre, S. A.; Rajwade, A. R.
1985
Evaluation of a cubic character sum using the $$\sqrt{-19}$$ division points of the curve $$y^ 2=x^ 3-2^ 3\cdot 19x+2\cdot 19^ 2$$. Zbl 0547.10033
Rishi, Dharam Bir; Parnami, J. C.; Rajwade, A. R.
1984
Criterion for 2 to be an $$\ell$$th power. Zbl 0539.10006
Parnami, J. C.; Agrawal, M. K.; Pall, Satinder; Rajwade, A. R.
1984
The number of points on the curve $$y^2=x^5+a$$ in $$\mathbb F_q$$ and application to local $$\zeta$$-function. Zbl 0556.14013
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1984
On the Jacobsthal sum $$\Phi_ 9(a)$$ and the related sum $$\psi_ 9(a)$$. Zbl 0512.10031
Katre, S. A.; Rajwade, A. R.
1983
Power stufe of Galois fields. Zbl 0603.12009
1983
Complex multipliction by $$(1+\sqrt{-19})/2$$. Zbl 0559.14029
Rishi, Dharam Bir; Parnami, J. C.; Rajwade, A. R.
1983
Jacobi sums and cyclotomic numbers for a finite field. Zbl 0491.12019
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1982
A new cubic character sum. Zbl 0488.10036
Rajwade, A. R.; Parnami, J. C.
1982
On expressing $$\sqrt{p}$$ as a rational linear combination of cosines of angles which are rational multiples of $$\pi$$. Zbl 0501.10016
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1982
On expressing a quadratic irrational as a rational linear combination of roots of unity. Zbl 0501.10017
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1982
On some trigonometric diophantine equations of the type $$\sqrt{n} = c_ 1 \cos \pi d_ 1 +\dots + c_\lambda \cos \pi d_\lambda$$. Zbl 0474.10018
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1981
A congruence relation between the coefficients of the Jacobi sum. Zbl 0483.12004
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1981
On the 4-power stufe of a field. Zbl 0493.10032
Parnami, J. C.; Agrawal, M. K.; Rajwade, A. R.
1981
The Diophantine equation $$y^2=x(x^2+21\,Dx+112\,D^2)$$ and the conjectures of Birch and Swinnerton-Dyer. Zbl 0382.14006
1977
Determination of a unique solution of the quadratic partition for primes $$p\equiv 1 (\mod 7)$$. Zbl 0366.10002
Nashier, Budh Singh; Rajwade, A. R.
1977
Some formulae for elliptic curves with complex multiplication. Zbl 0375.14011
1977
Some congruences in algebraic integers and rational integers. Zbl 0405.10004
1976
A note on the stufe of quadratic fields. Zbl 0363.12003
1975
Notes on the congruence $$y^2\equiv x^5-a\;(\mod p)$$. Zbl 0306.10004
1975
Certain classical congruences via elliptic curves. Zbl 0277.10028
1974
The number of solutions of the congruence $$y^2 \equiv x^4 - a (mod \;p)$$. Zbl 0298.10016
1974
On the congruence $$y^2 \equiv x^5 - a\pmod p$$. Zbl 0272.12001
1973
The number of solutions of the congruence $$y^2 \equiv x^6-a\pmod p$$. Zbl 0265.10002
1973
The period equation for primes $$p$$ congruent to $$1 (mod 5)$$. Zbl 0206.34601
1971
A note on the number of solutions $$N_ p$$ of the congruence $$y^ 2\equiv x^ 3-Dx (\mod p)$$. Zbl 0194.07901
1970
On rational primes p congruent to 1 (mod 3 or 5). Zbl 0182.07603
1969
Arithmetic on curves with complex multiplication by the Eisenstein integers. Zbl 0165.54804
1969
Arithmetic on corves with complex multiplication by $$\sqrt{-2}$$. Zbl 0188.25001
1968
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#### Cited by 75 Authors

 7 Baoulina, Ioulia N. 4 Katre, Shashikant A. 4 Rajwade, A. R. 4 Tanti, Jagmohan 3 Parnami, J. C. 3 Williams, Kenneth S. 2 Ahmed, Mohammad Helal Uddin 2 Anuradha, N. 2 Hoshi, Akinari 2 Jakubec, Stanislav 2 Morain, François 2 Pollack, Paul 2 Rubin, Karl Cooper 2 Silverberg, Alice 2 Sun, Zhihong 1 Adler, Allan 1 Amoroso, Francesco 1 Atkin, Arthur Oliver Lonsdale 1 Baccar, N. 1 Bakshi, Gurmeet K. 1 Berger, Arno 1 Berndt, Bruce Carl 1 Boston, Nigel 1 David, Sinnou 1 Dawsey, Madeline Locus 1 de Klerk, Etienne 1 Delzell, Charles N. 1 Do Duc, Tai 1 Dolcetti, Alberto 1 Dumir, Vishwa Chander 1 Evans, Ronald J. 1 Grahl, Jürgen 1 Hoffmann, Detlev W. 1 Hou, Xiang-Dong 1 Hu, Ya-Qing 1 Huang, Hua-Lin 1 Hudson, Richard H. 1 Humphries, Stephen P. 1 Juriaans, Stanley Orlando 1 Kałuszka, Marek 1 Krachun, Dmitry 1 Krzeszowiec, Michał 1 Lazarus, Andrew J. S. 1 Leep, David B. 1 Leprévost, Franck 1 Leung, Ka Hin 1 McCarthy, Dermot 1 Myerson, Gerald Ira 1 Nakazawa, Naoya 1 Nevo, Shahar 1 Olson, Loren D. 1 Ono, Ken 1 Parshin, Alexei N. 1 Pasechnik, Dmitrii V. 1 Passi, Inder Bir Singh 1 Pertici, Donato 1 Petrov, Fedor Vladimirovich 1 Pfister, Albrecht 1 Poulakis, Dimitrios 1 Prasad, Dipendra 1 Pumplün, Susanne 1 Raka, Madhu 1 Rishi, Dharam Bir 1 Scheiderer, Claus 1 Schmidt, Bernhard 1 Sharma, Anuradha 1 Souza Filho, A. C. 1 Stark, Harold M. 1 Tate, John Torrence jun. 1 van Wamelen, Paul B. 1 Vsemirnov, Maxim 1 Xia, LingLi 1 Yang, Jing 1 Zannier, Umberto M. 1 Zhang, Chi
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#### Cited in 36 Serials

 11 Journal of Number Theory 6 International Journal of Number Theory 4 Finite Fields and their Applications 3 Mathematics of Computation 3 Transactions of the American Mathematical Society 2 Rocky Mountain Journal of Mathematics 2 Inventiones Mathematicae 2 Journal of Algebra 2 Proceedings of the American Mathematical Society 2 Proceedings of the Japan Academy. Series A 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Journal de Théorie des Nombres de Bordeaux 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 American Mathematical Monthly 1 Indian Journal of Pure & Applied Mathematics 1 Israel Journal of Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematics Magazine 1 Journal of Soviet Mathematics 1 Manuscripta Mathematica 1 Pacific Journal of Mathematics 1 Tokyo Journal of Mathematics 1 Insurance Mathematics & Economics 1 Designs, Codes and Cryptography 1 Aequationes Mathematicae 1 European Journal of Operational Research 1 Linear Algebra and its Applications 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 The Ramanujan Journal 1 Journal of the Australian Mathematical Society 1 São Paulo Journal of Mathematical Sciences 1 Science China. Mathematics 1 Research in the Mathematical Sciences 1 Algebraic Combinatorics
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#### Cited in 15 Fields

 60 Number theory (11-XX) 17 Algebraic geometry (14-XX) 6 Field theory and polynomials (12-XX) 5 Combinatorics (05-XX) 4 Commutative algebra (13-XX) 3 Group theory and generalizations (20-XX) 3 Special functions (33-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Associative rings and algebras (16-XX) 1 History and biography (01-XX) 1 Real functions (26-XX) 1 Geometry (51-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)