Article PDF
Avoid common mistakes on your manuscript.
Literature cited
J. L. Lagrange, Oevres, T. 3, Gauthier-Villars, Paris (1896), pp. 189–201.
C. F. Gauss, Werke, Bd. 2, Göttingen (1863).
E. Artin, “Quadratische Körper im Gebiete der höheren Kongruenzen. II,” Math. Z.,19, 207–246 (1924).
H. Hasse, “Abstrakte Begründung der komplexen Multiplication und Riemannsche Vermutung in Funktionenkörper,” Abhand. Math. Sem. Univ. Hamburg,10, 325–348 (1934).
H. Hasse, “Zur Theorie der abstrakten elliptischen Funktionenkörper. I–III,” J. Reine Ang. Math.,175, 55–62, 69–88, 193–208 (1936).
Yu. I. Manin, “On congruences of the third degree with respect to a prime modulus,” Izv. Akad. Nauk SSSR, Ser. Mat.,20, 673–678 (1956).
A. Weil, “Sur les courbes algébriques et les variétés que s'en déduisent,” Act. Sci. Ind., 1041, Hermann, Paris (1948).
A. Weil, “On some exponential sums,” Proc. Nat. Acad. Sci.,34, No. 5, 204–207 (1948).
L. Carlitz and S. Uchiyama, “A bound for exponential sums,” Duke Math. J.,24, No. 1, 37–41 (1957).
L. Carlitz, “Kloosterman sums and finite field extensions,” Acta. Arithm.,16, No. 2, 179–193 (1969).
E. Bombieri, “On exponential sums in finite fields,” Am. J. Math.,88, No. 1, 71–105 (1966).
G. I. Perel'muter, “On some character sums,” Usp. Mat. Nauk,18, No. 2, 145–149 (1963).
M. Eichler, Einführung in die Theorie der algebraischen Zahlen und Funktionen, Basel-Stuttgart (1963).
S. Lang, Abelian Varieties, Wiley-Interscience, New York (1959).
A. G. Postnikov, “Ergodic problems in the theory of congruence and theory of Diophantine approximations,” Tr. Mat. Inst. Akad. Nauk SSSR,82 (1966).
H. M. Stark, “On the Riemann hypothesis in hyperelliptic function fields,” Proc. Symp. Pure Math.,24, 285–302 (1973).
N. M. Korobov, “An estimate for a sum of Legendre symbols,” Dokl. Akad. Nauk SSSR,196, No. 4, 764–767 (1971).
D. A. Mit'kin, “An estimate for a sum of Legendre symbols of polynomials of even degree,” Mat. Zametki,14, No. 1, 73–81 (1973).
W. M. Schmidt, “Zur Methode von Stepanov,” Acta. Arithm.,24, No. 4, 347–368 (1973).
W. M. Schmidt, “A lower bound for the number of solutions of equations over finite fields,” J. Number Theory,6, 448–480 (1974).
E. Bombieri, “Counting points on curves over finite fields (after S. A. Stepanov),” Sém. Bourbaki, Vol. 25, No. 430 (1972–73), pp. 234–241.
S. Lang and A. Weil, “Number of points of varieties in finite fields,” Amer. J. Math.,76, No. 4, 819–827 (1954).
S. A. Stepanov, “On the number of points of a hyperelliptic curve over a finite prime field,” Izv. Akad. Nauk SSSR, Ser. Mat.,33, No. 5, 1171–1181 (1969).
S. A. Stepanov, “Elementary method in the theory of congruences for a prime modulus,” Acta. Arithm.,17, No. 3, 231–247 (1970).
S. A. Stepanov, “An elementary proof of the Hasse-Weil theorem for hyperelliptic curves,” J. Number Theory,4, No. 2, 118–143 (1972).
S. A. Stepanov, “On an estimate for rational trigonometric sums with prime denominator,” Tr. Mat. Inst. Akad. Nauk SSSR,112, 346–372 (1971).
S. A. Stepanov, “Congruences with two unknowns,” Izv. Akad. Nauk SSSR, Ser. Mat.,36, 683–711 (1972).
S. A. Stepanov, “A constructive method in the theory of equations over finite fields,” Tr. Mat. Inst. Akad. Nauk SSSR,122, 237–246 (1973).
S. A. Stepanov, “Rational points of algebraic curves over finite fields,” in: Current Problems in Analytic Number Theory [in Russian], Minsk (1974), pp. 223–243.
S. A. Stepanov, “An elementary method in the theory of equations over finite fields,” in: Proc. Int. Cong. Mathematicians, Vancouver (1974), pp. 383–391.
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 24, No. 3, pp. 425–431, September, 1978.
Rights and permissions
About this article
Cite this article
Stepanov, S.A. An elementary method in algebraic number theory. Mathematical Notes of the Academy of Sciences of the USSR 24, 728–731 (1978). https://doi.org/10.1007/BF01097766
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097766