Khokiev Donier Jalilovich

Head of the Department, Candidate of Physical and Mathematical Sciences, Associate Professor.

Year of birth: 31.07.1991

Place of birth: Republic of Tajikistan

Nationality: Tajik

In 2014 he graduated with honors from the Faculty of Mechanics and Mathematics of the Tajik National University. 2014-2017 full-time postgraduate student of the A.Juraev Institute of Mathematics of the Academy of Sciences of the Republic of Tajikistan. In 2018, he defended his PhD thesis on the topic “On the distribution of values of Dirichlet characters by a composite module in a sequence of shifted primes”. Senior Lecturer of the Department of Algebra and Number Theory (2018-2022). Associate Professor, Head of the Department of Algebra and Number Theory (from 2022 to the present).

ABOUT THE ACTIVITIES OF THE DEPARTMENT

The Department of Algebra and Number Theory was founded in 1969. The founder and the first head was a specialist in the field of algebra and number theory, Professor Gafur Babayev. The heads of the department were also

- Doctor of Physical and Mathematical Sciences, Professor D.I. Ismoilov (1979-1995);
- Academician of the Academy of Sciences of the Republic of Tajikistan, Professor Z.H. Rakhmonov (1996-2007);
- Candidate of Physical and Mathematical Sciences, Associate Professor Sobirov A.Sh. (2007-2011);
- Candidate of Physical and Mathematical Sciences, associate Professor Boboerov Sh.K. (2011-2016).

• Candidate of Physical and Mathematical Sciences, Associate Professor Azamov A.Z. (2016-2021)

• Since 2022, the department is headed by Candidate of Physical and Mathematical Sciences, Associate Professor D.J. Khokiev.

Currently, the department employs 7 teachers, one Doctor of Sciences, academician of the Academy of Sciences of the Republic of Tajikistan and 6 Candidates of Sciences.

The Department at the Faculty of Mechanics and Mathematics and Physics provides teaching in the following subjects: algebra and number theory; analytical geometry, algebra and geometry; discrete mathematics and mathematical logic; linear algebra; special courses in algebra and number theory.

Research work at the department is carried out on the topic “Distribution of values of arithmetic functions”. Within the framework of this topic, research is conducted in all major areas of analytical number theory, and the most significant scientific achievements in the last 10 years are briefly characterized by the following indicators:

• asymptotic formulas in the Waring problem with almost equal terms are obtained;

• the theory of short trigonometric sums by G. Weyl was created;

• an asymptotic formula is found in the Esterman problem with almost equal terms on the representation of a sufficiently large natural number as the sum of two primes and the power of a natural number;

• an estimate of the sums of the values of Dirichlet’s non-main character in a sequence of shifted primes is obtained;

• an estimate of a short cubic trigonometric sum with a Mobius function in small arcs is found;

• the behavior of short G.Weyl sums with prime numbers is studied;

• an estimate is found from below of the length of the segment of the critical line in which the zero Riemann zeta function and the Davenport-Heilbronn function obviously exist.

These results have been published in the scientific journals “Proceedings of the Steklov Mathematical Institute”, “Reports of the Russian Academy of Sciences”, “Mathematical Notes”, “Chebyshev Collection” and in the publishing house “Springer”; they are an improvement and refinement of the relevant results of Academician I.M.Vinogradov, Professor A.A. Karatsuba, English mathematician R. Vaughn, Chinese mathematicians T. Zhang and J. Liu, Norwegian mathematician A. Selberg, Canadian mathematician J. B. Friedlander, American mathematician A.Kumchev and Australian mathematician I.E. Shparlinsky.

The Department cooperates with Lomonosov Moscow State University and the Steklov Institute of Mathematics. Within the framework of cooperation, joint research works, exchange of scientific information and training of personnel are carried out.

Rakhmonov Zarullo Husenovich, mathematician, Doctor of Physical and Mathematical Sciences, Academician of the Academy of Sciences of the Republic of Tajikistan. In 1982 he graduated from the Faculty of Mechanics and Mathematics, Lomonosov Moscow State University. In 1985 – 1996 assistant, senior lecturer, associate professor and professor of the Department of Algebra and Number Theory of TNU. Candidate of Physical and Mathematical Sciences (1986). Doctor of Physical and Mathematical Sciences (1996). Head of the Department of Algebra and Number Theory of TNU (1996 – 2007) and since 2007 Professor of the Department. Corresponding member of the Academy of Sciences of the Republic of Tajikistan (2000). Academician of the Academy of Sciences of the Republic of Tajikistan (2017). He was awarded the medal “20th Anniversary of Independence of the Republic of Tajikistan”