Selected publications - Doychin Tolev

Preprints

1.An identity for the Kloosterman sum , arXiv:math.NT/1007.2054v3.

2.On the number of pairs of positive integers x, y < H such that x^2 + y^2 + 1 is squarefree , arXiv:math.NT/1007.0353v1.

Scientific papers

1. On a version of Hua-lo-Ken's problem, (with A. Kirkoryan; in Russian). Math. Zametki, (in print).

2. On the number of pairs of positive integers x_1, x_2 < H such that x_1 x_2 is a k-th power ,
Pacific J. Math. (in print); arXiv:math.NT/0909.2811.

3 .On the distribution of $\alpha p$ modulo one for primes $p$ of a special form,

(with T.Todorova) , Mathematica Slovaca, (in print); arXiv:math.NT/0711.0171v2.

4. The ternary Goldbach problem with arithmetic weights attached to two of the variables,
J. Number Theory, 130, 2, (2010), 439-457.

          5. The binary Goldbach problem with arithmetic weights attached to one of the variables,
          Acta Arith. (in print); arXiv:0903.3128.

          6. The ternary Goldbach problem with primes from arithmetic progressions,
          Quarterly J. Math. (in print); arXiv:0902.2669.

          7. On the distribution of r-tuples of squarefree numbers in short intervals,
          International Journal of Number Theory, 2, (2006), 225-234.

          8.On the exceptional set of Lagrange’s equation with three prime and one almost-prime variables,
          J. Theorie Nombr. Bordeaux, 17, (2005), 925-948.

          9.On the exponential sum with squarefree numbers,
          Bull. London Math. Soc., 37, 6, (2005), 827-834.

          10.Lagrange’s four squares theorem with variables of special type,
          Bonner Math. Schriften, 360, 2003.

          11.Lagrange’s four squares theorem with one prime and three almost-prime variables,
          (with D. R. Heath–Brown), J. Reine Angew. Math. 558 (2003), 159–224.

          12. On a sum of five squares of primes, one of which belongs to an arithmetical progression,
          (with M.Laporta, in Russian) Fundam. Prikl. Math., 8, 1, (2002), 85–96.

          13. Additive problems with prime numbers of special type,
          Acta Arith. 96, 11 (2000), 53–88. Corrigendum: Acta Arith. 105, 2, (2002), 205.

          14. Representations of large integers as sums of two primes of special type,
          Algebraic number theory and Diophantine analysis (Graz, 1998), 485–495, de Gruyter, Berlin, 2000.

          15 .Arithmetic progressions of prime-almost-prime twins,
          Acta Arith. 88, 1, (1999), 67–98.

          16. An additive problem with primes and almost-primes,
          (with T. Peneva), Acta Arith. 83, 2, (1998), 155–169.

          17. On the number of representations of an odd integer as a sum of three primes, one of which belongs to an arithmetic progression,
          Proceedings of the Steklov Institute of Mathematics, 218, (1997), 415–432.

          18. An additive problem with prime numbers from a thin set,
          (with A. Kumchev), Acta Math. Hungar. 76, 1-2, (1997), 31–43.

          19. On a theorem of Bombieri-Vinogradov type for prime numbers from a thin set,
          Acta Arith. 81, 1, (1997), 57–68.

          20. On an equation with prime numbers, (with M. Laporta, in Russian), Math. Zametki 57, 6, (1995), 926–929.

          21. On a system of two Diophantine inequalities with prime numbers,
          Acta Arith. 69, 4, (1995), 387–400.

          22. On a Diophantine inequality involving prime numbers,
          Acta Arith. 61, 3, (1992), 289–306.

          23. Diophantine approximations with prime numbers near to squares,
          (in Russian), Matem. Zametki 50, 3, (1991), 129–134.

          24. On the simultaneous distribution of the fractional parts of different powers of prime numbers,
          J. Number Theory 37, 3, (1991), 298–306.

Surveys

          1.An invitation to additive prime number theory,
          (with A.Kumchev), Serdica Math. J., 31, (2005), 1001–1074.

          2. Goldbach's problems: past, present and future,
          (in Bulgarian), , Scientific Works of the 33 Spring conference of the UBM, (2004), 61-69.

Theses

          1.Additive problems in number theory,
          (in Russian), DSc Thesis , Lomonosov University University, Moscow, 2001.

          2. Diophantine inequalities with prime numbers,
          (in Russian), PhD Thesis , Moscow Lomonosov University, Moscow, 1990.

Textbooks

          1.Problems in number theory,
          (with N. Nachev, in Bulgarian), Plovdiv University Press, 2003.

          2.Additive problems in number theory, (in Bulgarian), Lecture notes, 2009.