Избрани публикации - Дойчин Толев

Препринти

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.


Научни стати

1.Об одной задачи Хуа-ло-Кена, (съвместно с А. Киркорян), Матем. Заметки, (в печат).

          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. (в печат); arXiv:math.NT/0909.2811.

          3.On the distribution of $\alpha p$ modulo one for primes $p$ of a special form,
          (съвместно с T. Тодорова), Mathematica Slovaca, (в печат); 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. (в печат); arXiv:0903.3128.

          6. The ternary Goldbach problem with primes from arithmetic progressions,
          Quarterly J. Math. (в печат); 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,
          (съвместно с D. R. Heath–Brown), J. Reine Angew. Math. 558 (2003), 159–224.

          12. О сумме пяти квадратов простых чисел, одно из которых принадлежит арифметической прогрессии,
          (съвместно с М. Лапорта) Фундам. Прикл. Мат. 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,
          (съвместно с Т. Пенева), 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,
          Труды матем. и-та им. Стеклова 218 (1997), Анал. теор. чисел и прилож., 415–432.

          18. An additive problem with prime numbers from a thin set,
          (съвместно с А. Кумчев), 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. Об одном уравнении с простыми числами,
          (съвместно с М. Лапорта), Матем. Заметки 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. Диофантовы приближения с простыми числами, близкими к квадратам,
          Матем. Заметки 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.

Обзорни статии

          1.An invitation to additive prime number theory,
          (съвместно с А. Кумчев), Serdica Math. J., 31, (2005), 1001–1074.

2. Проблеми на Голдбах - минало, настояще, бъдеще,
Научни трудове на 33 пролетна конференция на СМБ, Боровец 2004, 61-69.

Дисертации

1.Аддитивные задачи в теории чисел,
Докторска дисертация, МГУ "М. Ломоносов", Москва, 2001.

2. Диофантовы неравенства с простыми числами,
Канд. дисертация, МГУ "М. Ломоносов", Москва, 1990.

Учебни помагала

1. Ръководство по теория на числата,
(съвместно с Н. Начев), Пловдивско университетско издателство, 2003.

2.Адитивни задачи в теорията на числата, Записки по едноименния курс, 2009.