Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 48 Sayı: 2, 399 - 405, 01.04.2019

Öz

Kaynakça

  • E. Alkan, Values of Dirichlet L-functions, Gauss sums and trigonometric sums, Ra- manujan J. 26 (3), 375–398, 2011.
  • T. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, First edition, 1976.
  • B.C. Berndt, S. Kim and A. Zaharescu, The circle and divisor problems, and Ramanu- jan’s contributions through Bessel function series, The legacy of Srinivasa Ramanujan, 111–127, Ramanujan Math. Soc. Lect. Notes Ser. 20, Ramanujan Math. Soc. Mysore, 2013.
  • E. Bombieri and W. Gubler, Heights in Diophantine Geometry, in: New Mathematical Monographs, Cambridge University Press, 2006.
  • H. Davenport, Multiplicative Number Theory, Graduate Texts in Mathematics, Third edition, Springer, New York, 2000.
  • G.H. Hardy and E.M.Wright, An Introduction to the Theory of Numbers, 6th Edition, Oxford University Press, 2008.
  • K. Hentzelt and E. Noether, Zur Theorie der Polynomideale und Resultanten, Math. Ann. 88, 53–79, 1923.
  • G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95, 736–788, 1926.
  • J. Kollár, Sharp Effective Nullstellensatz, J. Amer. Math. Soc. 1 (4), 963–975, 1988.
  • A. Seidenberg, Constructions in algebra, Trans. Amer. Math. Soc. 97, 273–313, 1974.

Divisor function and bounds in domains with enough primes

Yıl 2019, Cilt: 48 Sayı: 2, 399 - 405, 01.04.2019

Öz

In this note, first we show that there is no uniform divisor bound for the Bézout identity using Dirichlet's theorem on arithmetic progressions. Then, we discuss for which rings the absolute value bound for the Bézout identity is not trivial and the answer depends on the number of small primes in the ring.

Kaynakça

  • E. Alkan, Values of Dirichlet L-functions, Gauss sums and trigonometric sums, Ra- manujan J. 26 (3), 375–398, 2011.
  • T. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, New York, First edition, 1976.
  • B.C. Berndt, S. Kim and A. Zaharescu, The circle and divisor problems, and Ramanu- jan’s contributions through Bessel function series, The legacy of Srinivasa Ramanujan, 111–127, Ramanujan Math. Soc. Lect. Notes Ser. 20, Ramanujan Math. Soc. Mysore, 2013.
  • E. Bombieri and W. Gubler, Heights in Diophantine Geometry, in: New Mathematical Monographs, Cambridge University Press, 2006.
  • H. Davenport, Multiplicative Number Theory, Graduate Texts in Mathematics, Third edition, Springer, New York, 2000.
  • G.H. Hardy and E.M.Wright, An Introduction to the Theory of Numbers, 6th Edition, Oxford University Press, 2008.
  • K. Hentzelt and E. Noether, Zur Theorie der Polynomideale und Resultanten, Math. Ann. 88, 53–79, 1923.
  • G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95, 736–788, 1926.
  • J. Kollár, Sharp Effective Nullstellensatz, J. Amer. Math. Soc. 1 (4), 963–975, 1988.
  • A. Seidenberg, Constructions in algebra, Trans. Amer. Math. Soc. 97, 273–313, 1974.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Haydar Göral 0000-0002-8814-6295

Yayımlanma Tarihi 1 Nisan 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 48 Sayı: 2

Kaynak Göster

APA Göral, H. (2019). Divisor function and bounds in domains with enough primes. Hacettepe Journal of Mathematics and Statistics, 48(2), 399-405.
AMA Göral H. Divisor function and bounds in domains with enough primes. Hacettepe Journal of Mathematics and Statistics. Nisan 2019;48(2):399-405.
Chicago Göral, Haydar. “Divisor Function and Bounds in Domains With Enough Primes”. Hacettepe Journal of Mathematics and Statistics 48, sy. 2 (Nisan 2019): 399-405.
EndNote Göral H (01 Nisan 2019) Divisor function and bounds in domains with enough primes. Hacettepe Journal of Mathematics and Statistics 48 2 399–405.
IEEE H. Göral, “Divisor function and bounds in domains with enough primes”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 2, ss. 399–405, 2019.
ISNAD Göral, Haydar. “Divisor Function and Bounds in Domains With Enough Primes”. Hacettepe Journal of Mathematics and Statistics 48/2 (Nisan 2019), 399-405.
JAMA Göral H. Divisor function and bounds in domains with enough primes. Hacettepe Journal of Mathematics and Statistics. 2019;48:399–405.
MLA Göral, Haydar. “Divisor Function and Bounds in Domains With Enough Primes”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 2, 2019, ss. 399-05.
Vancouver Göral H. Divisor function and bounds in domains with enough primes. Hacettepe Journal of Mathematics and Statistics. 2019;48(2):399-405.