Author: Y. C. Wang 1
View More View Less
  • 1 School of Mathematics, Shandong University, Jinan Shandong 250100, China
Restricted access

Abstract

Let denote the set {n∣2|n, ∀ p>2 with p−1|k}. We prove that when , almost all integers can be represented as the sum of a prime and a k-th power of prime for k≧3. Moreover, when , almost all integers n∊(X,X+H] can be represented as the sum of a prime and a k-th power of integer for k≧3.

  • [1] Baker, R. C. Harman, G. Pintz, J. 1997 The exceptional set for Goldbach's problem in short intervals Sieve Methods, Exponential Sums and their Applications in Number Theory 154 . Cambridge University Press.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2] Bauer, C. 1998 On the sum of a prime and the k-th power of a prime Acta Arith. 85 99118.

  • [3] Gallagher, P. X. 1970 A large sieve density estimate near σ=1 Invent. Math. 11 329339 .

  • [4] Hua, L. K. 1938 Some results in prime number theory Q.J. Math. 9 6880 .

  • [5] Jia, C. H. 1995 Goldbach numbers in a short interval (I) Sci. China Ser. A 38 385406.

  • [6] Jia, C. H. 1995 Goldbach numbers in a short interval (II) Sci. China Ser. A 38 513523.

  • [7] Jia, C. H. 1996 On the exceptional set of Goldbach numbers in a short interval Acta Arith. 77 207287.

  • [8] Kumchev, A. V. 2006 On Weyl sums over primes and almost primes Michigan Math. J. 54 243268 .

  • [9] Kumchev, A. V. Liu, J. Y. 2009 Sums of primes and squares of primes in short intervals Monatsh. Math. 157 335363 .

  • [10] Li, H. Z. 1995 Goldbach numbers in a short interval Sci. China Ser. A 38 641652.

  • [11] Liu, J. Y. Zhan, T. 1997 On a theorem of Hua Arch. Math. (Basel) 69 375390 .

  • [12] Mikawa, H. 1992 On the exceptional set in Goldbach's problem Tsukuba J. Math. 16 513543.

  • [13] Perelli, A. Pintz, J. 1993 On the exceptional set for Goldbach's problem in short intervals J. London Math. Soc. 47 4149 .

  • [14] Perelli, A. Zaccagnini, A. 1995 On the sum of a prime and a k-th power Izv. Ross. Akad. Nauk Mat. 59 185200.

  • [15] Ramachandra, K. 1973 On the number of Goldbach numbers in small intervals J. Indian Math. Soc. 37 157170.

  • [16] Saffari, B. Vaughan, R. C. 1977 On the fractional parts of x/n and related sequences. II Ann. Inst. Fourier (Grenoble) 27 130 .

  • [17] Schwarz, W. 1961 Zur Darstellung von Zahlen durch Summen von Primzahlpotenzen. II J. Reine Angew. Math. 206 78112.

  • [18] Titchmarsh, E. C. 1986 The Theory of the Riemann Zeta-Function 2 Clarendon Press Oxford.

  • [19] Zaccagnini, A. 1992 The exceptional set for the sum of a prime and a k-th power Mathematika 39 400421 .

Acta Mathematica Hungarica
P.O. Box 127
HU–1364 Budapest
Phone: (36 1) 483 8305
Fax: (36 1) 483 8333
E-mail: acta@renyi.mta.hu

  • Impact Factor (2019): 0.588
  • Scimago Journal Rank (2019): 0.489
  • SJR Hirsch-Index (2019): 38
  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

For subscription options, please visit the website of Springer Nature

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
May 2021 0 0 0
Jun 2021 1 0 0
Jul 2021 0 0 0
Aug 2021 0 0 0
Sep 2021 1 0 0
Oct 2021 0 0 0
Nov 2021 0 0 0