Autors: Dimitrov, S. I.
Title: Barban–Davenport–Halberstam Type Theorems for Exponential Sums and Piatetski-Shapiro Primes
Keywords: Barban–Davenport–Halberstam theorem, exponential sums over primes, generalized Riemann hypothesis, large sieve, Piatetski-Shapiro primes

Abstract: In this paper we establish three Barban–Davenport–Halberstam type theorems. Namely for exponential sums over primes, for Piatetski-Shapiro primes and for exponential sums over Piatetski-Shapiro primes.

References

  1. H. Davenport Multiplicative number theory 3 Cham Springer
  2. S.I. Dimitrov A ternary diophantine inequality by primes with one of the form p=x2+y2+1 Ramanujan J. 59 2 571 607 4480301 10.1007/s11139-021-00545-1
  3. S.I. Dimitrov A Bombieri - Vinogradov type result for exponential sums over Piatetski-Shapiro primes Lith. Math. J. 62 4 435 446 4515118 10.1007/s10986-022-09579-4
  4. S.W. Graham G. Kolesnik Van der Corput’s Method of Exponential Sums New York Cambridge University Press 10.1017/CBO9780511661976
  5. C. Hooley On the Barban-Davenport-Halberstam theorem I J. Reine Angew. Math. 274 275 206 223 382202
  6. H. Iwaniec E. Kowalski Analytic number theory, Colloquium Publications Rhode Island American Mathematical Society
  7. A. Kumchev Z. Petrov A hybrid of two theorems of Piatetski-Shapiro Monatsh. Math. 189 355 376 3949736 10.1007/s00605-018-1217-4
  8. J. Li F. Xue M. Zhang A ternary Diophantine inequality with prime numbers of a special form Period. Math. Hungar. 85 1 14 31 4469414 10.1007/s10998-021-00415-9
  9. J. Li M. Zhang F. Xue An additive problem over Piatetski-Shapiro primes and almost-primes Ramanujan J. 57 1307 1333 4394008 10.1007/s11139-021-00390-2
  10. Y. Lu An additive problem on Piatetski-Shapiro primes Acta Math. Sin. (Engl. Ser.) 34 255 264 3750396 10.1007/s10114-017-7030-5
  11. H. Montgomery Primes in arithmetic progressions Michigan Math. J. 17 33 39 257005 10.1307/mmj/1029000373
  12. T. Peneva An additive problem with Piatetski-Shapiro primes and almost-primes Monatsh. Math. 140 119 133 2017664 10.1007/s00605-002-0005-2
  13. I.I. Piatetski-Shapiro On the distribution of prime numbers in sequences of the form [f(n)] Mat. Sb. 33 559 566 59302
  14. X. Wang Y. Cai An additive problem involving Piatetski-Shapiro primes Int. J. Number Theory 7 1359 1378 2825977 10.1142/S1793042111004630
  15. J. Rivat P. Sargos Nombres premiers de la forme [nc] Canad. J. Math. 53 414 433 1820915 10.4153/CJM-2001-017-0
  16. J. Rivat J. Wu Prime numbers of the form [nc] Glasg. Math. J 43 237 254 1838628 10.1017/S0017089501020080
  17. D. Tolev On a diophantine inequality involving prime numbers Acta Arith. 61 289 306 1161480 10.4064/aa-61-3-289-306
  18. D. Tolev On a diophantine inequality with prime numbers of a special type Proc. Steklov Inst. Math. 299 261 282 3761457 10.1134/S0081543817080168
  19. J.D. Vaaler Some extremal functions in Fourier analysis Bull. Amer. Math. Soc. 12 183 216 776471 10.1090/S0273-0979-1985-15349-2
  20. Zhu, L.: A ternary diophantine inequality with prime numbers of a special type, Proc. Indian Acad. Sci. Math. Sci., 130, (2020), Art. 23

Issue

Results in Mathematics, vol. 80, 2025, Switzerland, https://doi.org/10.1007/s00025-025-02403-8

Вид: статия в списание, публикация в издание с импакт фактор, публикация в реферирано издание, индексирана в Scopus и Web of Science