Alexandru Zaharescu

Address:

Institute of Mathematics of the Romanian Academy
P.O. Box 1-764, RO-70700 Bucharest, Romania

Education:

• BS: University of Bucharest, Faculty of Mathematics 1986
• PhD: University of Bucharest, 1991, thesis advisor: Professor Nicolae Popescu
• PhD: Princeton University, 1995, thesis advisor: Professor Peter Sarnak

Employment:

• 1986-1988: Teacher, High School No. 1, Codlea, Romania
• 1988-present: Researcher, INCREST, Dept. of Mathematics (IMAR after 1990)
• 1995 - June 1998: CLE Moore Instructor, Department of Mathematics, Massachusetts Institute of Technology
• August 1998 - June 1999: Postdoctoral Fellow, Department of Mathematics and Statistics, McGill University
• October 1999-June 2000: Member, Institute for Advanced Study, Princeton, USA

Publications:

1. Graph-continuous functions, (Romanian) Stud. Cerc. Mat. 35 (1983), no. 1, 89-100.
2. Representation of arbitrary functions by graph-continuous Darboux functions, (Romanian) Stud. Cerc. Mat. 35 (1983), no. 2, 161-168.
3. On a conjecture of Graham, J. Number Theory 27 (1987), 33-40.
4. A theorem of characterization of residual transcendental extensions of a valuation, J. Math. Kyoto Univ., 28 (1989), 579-592. (with V. Alexandru and N. Popescu)
5. Graham's Conjecture under Riemann Hypothesis, J. Number Theory, 31 (1989), 80-87. (with C. Cobeli and M. Vajaitu)
6. Minimal pairs of definition of a residual transcendental extension of a valuation, J. Math. Kyoto Univ., 30 (1990), 207-225. (with V. Alexandru and N. Popescu)
7. All valuations on K(X), J. Math. Kyoto Univ., 30 (1990), 281-296. (with V. Alexandru and N. Popescu)
8. Ilieff's Conjecture on a Corona, Bull. London Math. Soc., 25 (1993), 49-54. (with V. Vajaitu)
9. On a class of valuations on $K(X)$, An. St. Univ. Ovidius Constantza, 2 (1994), 120-136. (with N. Popescu)
10. Completions of r.a.t.-Valued Fields of Rational Functions, J. Number Theory, 50 (1995) 202-205. (with A. Iovita)
11. On the structure of Irreducible Polynomials over Local Fields, J. Number Theory, 52 (1995), 98-118. (with N. Popescu)
12. Nondiscrete local ramified class field theory, J. Math. Kyoto Univ., 35 (1995), 325-339. (with A. Iovita)
13. Small values of $n^2\alpha (mod 1)$, Invent. math., 121 (1995), 379-388.
14. On the main invariant of an element over a local field, Portugaliae Mathematica, 54 (1997), 73-83. (with N. Popescu)
15. Facteurs de type III associés aux ensembles de nombres premiers, C. R. Acad. Sci. Paris, 324 (1997), 797-800. (with F. Boca)
16. On the distribution of primitive roots mod $p$, Acta Arith. 83 (1998), no. 2, 143-153. (with C. Cobeli)
17. On the closed subfields of $C_p$, J. Number Theory 68 (1998), no. 2, 131-150. (with V. Alexandru and N. Popescu)
18. On the roots of a class of lifting polynomials, Seminarberichte aus dem Fachbereich Mathematik, Band 63 (1998), Teul 4, 587-600. (with N. Popescu)
19. Galois theory for $B_{dR}^+$, Compositio Math. 117, 1999, no. 1, 1-33. (with A. Iovita)
20. On a class of exponential congruences, Proc. Amer. Math. Soc. 127 (1999), no. 8 , 2225-2232 (with M. Vajaitu)
21. Averages of short exponential sums, Acta Arithmetica 88 (1999), no. 3, 223-231
22. A metric result on the pair correlation of fractional parts of sequences, Acta Arithmetica 89 (1999) no. 3, 283-293 (with Z. Rudnick)
23. Generating elements for $B_{dR}^+$, J. Math. Kyoto Univ., 39 (1999) no. 2, 233-249 (with A. Iovita)
24. An exponential congruence with solutions in primitive roots, Rev. Roumaine Math. Pures Appl., 44 (1999), 1, 15-22. (with C. Cobeli)
25. Type III factors and the distribution of prime numbers, Proc. London Math. Soc., 80 (2000), no. 1, 145-178 (with F. Boca)
26. Density of zeros of $L(s,\chi)$ near $s=1$ and the smallest character nonresidue, C. R. Math. Rep. Acad. Sci. Canada, 22 (2000) no. 1, 7-12.
27. The sequence n! (mod p), J. Ramanujan Math. Soc., 15 (2000) no. 2, 71-90. (with C. Cobeli and M. Vajaitu)
28. A cellular automaton on a torus, to appear in Portugaliae Math. (with M. Crasmaru and C. Cobeli)
29. The generating degree of $C_p$, to appear in Canad. Math. Bull. (with V. Alexandru and N. Popescu)
30. A metric symbol for pairs of polynomials over local fields, to appear in C. R. Math. Rep. Acad. Sci. Canada.
31. Erdos-Turan inequality in p-adic fields, to appear in Math. Reports. (with M. Vajaitu)
32. Exponential sums and their role in number theory (I), to appear in Rev. Roumaine. (with M. Vajaitu)
33. Pair correlation of values of rational functions (mod p), to appear in Duke Math. Journal. (with F. Boca)
34. The order of inverses mod q, to appear in Mathematika. (with C. Cobeli)
35. The analytic continuation problem for $p-$adic $L-$functions, to appear in Math Reports. (with M. Vajaitu)
36. The distribution of spacings between small powers of a primitive root, to appear in Israel J. Math. (with Z. Rudnick)
37. Distribution of lattice points visible from the origin, to appear in Comm. in Math. Phys. (with F. Boca and C. Cobeli)
38. Exponential sums and their role in number theory (II), to appear in Rev. Roumaine. (with M. Vajaitu)
39. The $h$-spacing distribution between Farey points, to appear in Cambridge Phil. Soc. Math. Proc. (with V. Augustin, F. Boca and C. Cobeli)
40. Trace on $C_p$, to appear in J. Number Theory. (with V. Alexandru and N. Popescu)
41. Integer points unusually close to elliptic curves, to appear in Portugaliae Math. (with M. Vajaitu)
42. Explicit formulas for the pair correlation of zeros of functions in the Selberg class, to appear in Forum Mathematicum. (with R. Murty)
43. Distribution of a sparse set of fractions mod p, to appear in Bull. London Math. Soc. (with C. Cobeli)
44. A question of Granville and its generalization, to appear in Acta Arithmetica. (with C. Cobeli)