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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 5, Pages 1171–1181 (Mi izv2197)  

This article is cited in 16 scientific papers (total in 16 papers)

On the number of points of a hyperelliptic curve over a finite prime field

S. A. Stepanov


Abstract: A new method is proposed in this paper for investigating algebraic congruences with prime modulus, leading in the case of hyperelliptic curves to estimates of the same order of strength as the classical estimates of Hasse and Weil.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:5, 1103–1114

Bibliographic databases:

UDC: 511
MSC: 14H52, 14H10, 11C08
Received: 24.09.1968

Citation: S. A. Stepanov, “On the number of points of a hyperelliptic curve over a finite prime field”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 1171–1181; Math. USSR-Izv., 3:5 (1969), 1103–1114

Citation in format AMSBIB
\Bibitem{Ste69}
\by S.~A.~Stepanov
\paper On the number of points of a~hyperelliptic curve over a~finite prime field
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 5
\pages 1171--1181
\mathnet{http://mi.mathnet.ru/izv2197}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=252400}
\zmath{https://zbmath.org/?q=an:0192.58002}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 5
\pages 1103--1114
\crossref{https://doi.org/10.1070/IM1969v003n05ABEH000834}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Stepanov, “Estimation of Weyl sums with prime denominator”, Math. USSR-Izv., 4:5 (1970), 1017–1041  mathnet  crossref  mathscinet  zmath
    2. S. A. Stepanov, “Congruences in two unknowns”, Math. USSR-Izv., 6:4 (1972), 677–704  mathnet  crossref  mathscinet  zmath
    3. I. E. Shparlinski, “On some problems in the theory of finite fields”, Russian Math. Surveys, 46:1 (1991), 199–240  mathnet  crossref  mathscinet  zmath  adsnasa
    4. Yu. V. Malykhin, “Bounds for exponential sums modulo $p^2$”, J. Math. Sci., 146:2 (2007), 5686–5696  mathnet  crossref  mathscinet  zmath  elib  elib
    5. Antonio Cafure, Guillermo Matera, “Improved explicit estimates on the number of solutions of equations over a finite field”, Finite Fields and Their Applications, 12:2 (2006), 155  crossref
    6. L. P. Bocharova, N. M. Dobrovolskii, I. Yu. Rebrova, “Pyatdesyat let teoretiko-chislovomu metodu v priblizhennom analize: problemy i dostizheniya”, Chebyshevskii sb., 8:4 (2007), 4–49  mathnet
    7. A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters”, Russian Math. Surveys, 63:4 (2008), 641–690  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. Machiel Van Frankenhuijsen, “The two-variable zeta function and the Riemann hypothesis for function fields”, Expositiones Mathematicae, 26:3 (2008), 249  crossref
    9. M. Z. Garaev, “Sums and products of sets and estimates of rational trigonometric sums in fields of prime order”, Russian Math. Surveys, 65:4 (2010), 599–658  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. P. X. Gallagher, H. L. Montgomery, “A Note on Burgess's Estimate”, Math. Notes, 88:3 (2010), 321–329  mathnet  crossref  crossref  mathscinet  isi
    11. I. V. Vyugin, I. D. Shkredov, “On additive shifts of multiplicative subgroups”, Sb. Math., 203:6 (2012), 844–863  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “Intersections of Shifts of Multiplicative Subgroups”, Math. Notes, 100:2 (2016), 189–198  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “On the Additive Energy of the Heilbronn Subgroup”, Math. Notes, 101:1 (2017), 58–70  mathnet  crossref  crossref  mathscinet  isi  elib
    14. Yazici E.A., Murphy B., Rudnev M., Shkredov I., “Growth Estimates in Positive Characteristic Via Collisions”, Int. Math. Res. Notices, 2017, no. 23, 7148–7189  crossref  isi
    15. S. S. Demidov, E. A. Morozova, V. N. Chubarikov, I. Yu. Rebrova, I. N. Balaba, N. N. Dobrovolskii, N. M. Dobrovolskii, L. P. Dobrovolskaya, A. V. Rodionov, O. A. Pikhtilkova, “Teoretiko-chislovoi metod v priblizhennom analize”, Chebyshevskii sb., 18:4 (2017), 6–85  mathnet  crossref  elib
    16. I. V. Vyugin, “A Bound for the Number of Preimages of a Polynomial Mapping”, Math. Notes, 106:2 (2019), 203–211  mathnet  crossref  crossref  mathscinet  isi  elib
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