## Prof. GEORGE LOMADZE## CURRICULUM VITAE |

**AFFILATION**

University str. 2

380043 Tbilisi, Georgia

**PERSONAL DATA**

Birthdate: December 27, 1912

Birthplace: Moscow, Russia

Nationality: Georgian

**EDUCATION AND SCIENTIFIC DEGREES**

1932-1937 | Student of Tbilisi State University, Faculty of Physics and Mathematics |

1937 | Diploma in Mathematics (with honour), Tbilisi State University |

1938 | Post-graduate student of A. Razmadze Mathematical Institute |

1948 | Kandidat of Mathematics, A. Razmadze Mathematical Institute |

1963 | Doctor of Sciences (Phys. and Math.), Leningrad State University |

**LANGUAGES**

Georgian, Russian, French

**POSITIONS HELD AND ACADEMIC EXPERIANCE**

1941-1946 | Service in Soviet Armed Forces |

1946-1953 | researcher of A. Razmadze Math. Institute |

1948-1965 | Assistent Professor of Tbilisi State University |

1965-up to now | Full Professor of Tbilisi State University |

**RESEARCH INTERESTS**

Analytic Number Theory (Representations of numbers by quadratic forms with integral coefficients, entire modular forms)

**SUPERVISION OF POST-GRADUATE STUDENTS**

R. Gongadze - | defended the Kandidat degree in 1963 at Tbilisi State University |

R. Beridze - | defended the Kandidat degree in 1965 at Tbilisi State University |

T. Vepkhvadze - | defended the Kandidat degree in 1970 at Tbilisi State University |

G. Gogishvili - | defended the Kandidat degree in 1971 at Tbilisi State University |

L. Sulakvelidze - | defended the Kandidat degree in 1978 at Tbilisi State University |

K. Shavgulidze - | defended the Kandidat degree in 1989 at Tbilisi State University |

N. Katchakhidze - | defended the Kandidat degree in 1993 at Tbilisi State University |

**PARTICIPATION IN CONFERENCES AND OTHER SCIENTIFIC FORUMS**

- Third all-union mathematical congress, Moscow 1956
- Fourth all-union mathematical congress, Leningrad 1961
- International congress of mathematicians, Moscow 1966
- Higher school conference in Number Theory, Vladimir 1968
- All-union simposium in Number Theory, Alma-Ata 1969
- International conference in Number Theory, Moscow 1971
- All-union conference in Number Theory, Samarkand 1972
- All-union conference in Analytic Number Theory, Vilnius 1974
- All-union school-seminar in Number Theory, Dushanbe 1977
- All-union conference in Number Theory, Tbilisi 1985
- All-union school in Number Theory, Minsk 1989
- International conference in Analytic and Probabilistic Number Theory, Vilnius 1991
- First congress of mathematicions of Georgia, Tbilisi 1994
- Second Congress of mathematicions of Georgia, Tbilisi 1997

- On the representation of numbers by squares, Trudy Tbiliss. Mat. Inst., 16 (1948), pp. 231-275 (in Russian).
- On the representation of numbers by an odd number of squars, Trudy Tbiliss. Mat. Inst., 17 (1949), pp. 281-314 (in Russian).
- On simulteneous representation of two integers by sums of integers and their squares, Trudy Tbiliss. Mat. Inst., 18 (1951), pp. 153-181 (in Russian).
- On summation of one singular series, Trudy Tbiliss. Mat. Inst., 19 (1953), pp. 61-77 (in Russian).
- On summation of one singular series: II, Trudy Tbiliss. Mat. Inst., 20 (1954), pp. 21-45 (in Russian).
- On the representation of numbers by squares, Trudy Tbiliss. Mat. Inst., 20 (1954), pp. 47-87 (in Russian).
- On the representation of numbers by sums of generalized polygonal integers, Trudy Tbiliss. Mat. Inst., 22 (1956), pp. 77-102 (in Russian).
- On the representation of numbers by sums of generalized polygonal integers: II, Trudy Tbiliss. Mat. Inst., 24 (1957), pp. 3-33 (in Russian).
- On the representation of numbers by sums of generalized polygonal integers, Trudy Tbiliss. Univ., 64 (1957), pp. 81-91 (in Russian).
- Über die Darstellung der Zahlen durch einige quaternäre quadratische Formen, Acta Arithmetica, 5 (1959), pp. 125-170.
- On the representation of numbers by some quadratic forms in four variables, Trudy Tbiliss. Univ., 76 (1959), pp. 108-159 (in Russian).
- On the representation of numbers by some ternary quadratic forms, Trudy Tbiliss. Mat. Inst., 27 (1960), pp. 115-141 (in Russian).
- Über die Darstellung der Zahlen durch einige ternäre quadratische Formen, Acta Arithmetica, 6 (1961), pp. 225-275.
- On the representation of numbers by binary quadratic forms, Trudy Tbiliss. Univ., 84 (1961), pp. 285-290 (in Russian).
- The scientific work of Arnold Walfisz, Acta Arithmetica, 10 (1964), pp. 227-237.
- On the representation of numbers by some quaternary quadratic forms, Trudy Tbiliss. Univ., 110 (1965), pp. 163-180 (in Russian).
- On the representation of numbers by positive binary diagonal quadratic forms, Mat. Sbornik, 68 (1965), pp. 282-312 (in Russian).
- On the arithmetical sense of some coefficients, Bull. Acad. Sci. Georgian SSR, 41 (1966), pp. 257-263 (in Russian).
- On the representation of numbers by some quadratic forms in six variables, Trudy Tbiliss. Univ., 117 (1966), pp. 9-43 (in Russian).
- On the representation of numbers by some quadratic forms in six variables: II, Trudy Tbiliss. Univ., 129 (1968), pp. 275-297 (in Russian).
- On the representation of numbers by some quadratic forms in four variables, Bull. Acad. Sci. Georgian SSR, 50 (1968), pp. 295-300 (in Russian).
- On the representation of numbers by the forms
*x*_{1}^{2}+ 3*x*_{2}^{2}+ 36*x*_{3}^{2}and*x*_{1}^{2}+ 12*x*_{2}^{2}+ 36*x*_{3}^{2}, Bull. Acad. Sci. Georgian SSR, 51 (1968), pp. 25-30 (in Russian). - On the representation of numbers by some binary quadratic forms, Izvestiya Vyssh. Ycheb. Zav. (Matematika), 11 (1970), pp. 71-75 (in Russian).
- On the representation of numbers by positive ternary diagonal quadratic forms: I, Acta Arithmetica, 19 (1971), pp. 267-305 (in Russian).
- On the representation of numbers by positive ternary diagonal quadratic forms: II, Acta Arithmetica, 19 (1971), pp. 387-407 (in Russian).
- On the number of representations of numbers by quadratic forms in four variables, 40 (1971), Trudy Tbiliss. Mat. Inst., 40 (1971), pp. 106-139 (in Russian).
- Formulas for the number of representations of numbers by all primitive positive ternary diagonal quadratic forms belonging to one class genera, Trudy Tbiliss. Mat. Inst., 40 (1971), pp. 140-179 (in Russian).
- On behaviour of the derivatives of Theta-functions under linear substitutions, Trudy Tbiliss. Univ., 146 (1972), pp. 15-27 (in Russian).
- On the basis of the space of spherical functions of fourth order relative to a positif quadratic form, Bull. Acad. Sci. Georgian SSR, 69 (1973), pp. 533-536 (in Russian).
- On the number of representations of numbers by positive quadratic forms in six variables, Trudy Tbiliss. Mat. Inst., 45 (1974), pp. 111-133 (in Russian).
- On the basis of the space of spherical functions relative to a positif quadratic form, Trudy Tbiliss. Mat. Inst., 45 (1974), pp. 134-145 (in Russian).
- On cusp forms of prime level and principal type, Trudy Tbiliss. Mat. Inst., 45 (1974), pp.146-161 (in Russian).
- On representation of numbers by sum of 8
*t*+ 1 squares, Trudy Tbiliss. Univ., 179 (1976), pp. 63-66 (in Russian). - Formulas for the number of representations of numbers by some regular and semiregular ternary quadratic forms belonging to two class genera, Acta Arithmetica, 34 (1978), pp. 131-162 (in Russian).
- On cusp forms of prime level and neighbouring type, Trudy Tbiliss. Mat. Inst., 63 (1980), pp. 36-53 (in Russian).
- On cusp forms of prime level and principal type: II, Trudy Tbiliss. Mat. Inst., 57 (1977), pp. 63-81 (in Russian).
- On cusp forms of prime level and neighbouring type: II, Trudy Tbiliss. Mat. Inst., 72 (1983), pp. 40-54 (in Russian).
- On cusp and quadratic forms of prime level and neighbouring type: I, Trudy Tbiliss. Mat. Inst., 84 (1987), pp. 36-54 (in Russian).
- On the representation of numbers by sums of quadratic
forms
*x*_{1}^{2}+*x*_{1}*x*_{2}+*x*_{2}^{2}, Acta Arithmetica, 54 (1989), pp. 9-36 (in Russian). - On the representation of numbers by a direct sum of quadratic
forms
*x*_{1}^{2}+*x*_{1}*x*_{2}+*x*_{2}^{2}, Trudy Tbiliss. Univ., 288 (1989), pp. 5-21 (in Russian). - On the representation of numbers by a direct sum of quadratic
forms
*x*_{1}^{2}+*x*_{1}*x*_{2}+*x*_{2}^{2}, Trudy Tbiliss. Univ., 289 (1990), pp. 12-58 (in Russian). - On cusp and quadratic forms of prime level and neighbouring type: II, Trudy Tbiliss. Mat. Inst., 104 (1993), pp. 53-66 (in Russian).
- On some arithmetical applications of the theory of modular forms, Trudy V. Steklov Mat. Inst., 200 (1991), pp. 236-244 (in Russian).
- On some entire modular forms of half integral weight for the group
G
_{0}(4*N*), New trends in Probab. and Statist., (1992), pp. 57-67. - On the number of representations of natural numbers by sums of nine squares, Acta Arithmetica, 68 (1994), pp. 245-253 (in Russian).
- On some entire modular forms of weight 5 and 6 for the congruence
group G
_{0}(4*N*), Georgian Math. J., 1 (1994), pp. 53-76. - Construction of entire modular forms of weights 5 and 6
for the congruence group G
_{0}(4*N*), Georgian Math. J., 1 (1995), pp. 189-199. - On the number of representations of integers by some quadratic forms in ten variables, Georgian Math. J., 2 (1995), pp.491- 516.
- On some entire modular forms of weight 7/2 and 9/2 for the congruence
group G
_{0}(4*N*), Georgian Math. J., 3 (1996), pp. 485-500. - On the number of representations of positive integers by a direct sum of binary quadratic forms with discriminant -23, Georgian Math, J., 4 (1997), pp. 523-532.