Umberto Zannier, pubblicazioni
Lista delle pubblicazioni:
[1] - Una proprietà aritmetica dei polinomi, (con A.Perelli),
Boll. U.M.I.
(5) 17-A, (1980).
[2] - Su un teorema di Pólya, (con A.Perelli), Boll. U.M.I., (
5),
18/A, (1981).
[3] - A note on the arithmetic properties of certain recurrence sequences,
(con
A. Perelli), Coll. Math. Soc. Janos Bolyai, 34, Topics in Classical
Number Theory, Budapest 1981, 1209-1215.
[4] - On periodic mod p sequences, (con A.Perelli) , Journal of Number
Theory, 15 (1982).
[5] - A note on recurrent mod p sequences, Acta Arith., XLI
(1982).
[6] - On the distribution of self numbers, Proc. Amer. Math. Soc.,
(85),
1, (1982).
[7] - On sums of distinct integers belonging to certain sequences, (con
A. Perelli), Acta Math. Hung., 41, (3-4) (1983), 251-254.
[8] - On polynomials taking small values at integral arguments, (con
R.Dvornicich), Acta Arith., XLII, (1983), 189-196.
[9] - Sulla parità di [nÖ2], (con A.Perelli), Boll. U.M.I.,
2/A
(1983).
[10] - Arithmetic properties of certain recurrence sequences, (con A.Perelli)
Journal Australian Math. Soc., 37 (1984), 4-16.
[11] - On recurrent mod p sequences, (con A. Perelli), Journal reine
angew.
Math., 348 (1984), 135-146.
[12] - Su un'equazione funzionale legata agli omomorfismi di un gruppo in un
corpo, (con A.Perelli), Boll. U.M.I. (6) 5/B (1986)
[13] - An W result in uniform distribution theory, (con A.Perelli),
Quart. J. Math., Oxford, 38 (1987), 95-102.
[14] - Sugli insiemi piccoli in un gruppo, (con A.Vitolo), Rendiconti
Acc. Naz. dei Lincei, CCCLXXXV (1988), 413-418.
[15] - An amusing problem about quadruples of real numbers, Ricerche di
Matematica, 37 (1988), 113-119.
[16] - On a theorem of Birch concerning sums of distinct terms from a given
sequence of integers, Math. Proc. Camb. Phil. Soc., 106 (1989),
199-206.
[17] - An extremal property of the Moebius function, (con A.Perelli),
Archiv
der Math., 53 (1989), 20-29.
[18] - On the linear independence of roots of unity over finite extensions of
Q, Acta Arith., LII, (1989), 171-182.
[19] - On the vector space of translates of a map from an abelian group into a
field of positive characteristic, (con. P. Zanardo), Boll. U.M.I.,
(7)
3-B (1989), 109-123.
[20] - An inequality for the Height of the powers of a polynomial, (con
A. Vitolo), Boll.U.M.I. (7) 4-A (1990), 399-403.
[21] - Inequalities for superadditive functions related to a property of
convex sets, (con A.Vitolo), Boll. U.M.I., (7) 4-A (1990)
[22] - The group of Pythagorean triples in number fields, (con P. Zanardo),
Annali di Matematica pura ed applicata, CLIX (1991),
81-88.
[23] - A note on incomplete quadratic Gauss sums, (con F. Sullivan),
Boll. U.M.I. (7) 6-A (1992), 49-57.
[24] - Distribution of solutions of diophantine equations f1(x1)f2(x2) = f3(x3) where fi are polynomials, (con A. Schinzel),
Rend. Sem. Mat. Univ. Padova, 87 (1992), 39-68.
[25] - An elementary proof of some results concerning sums of distinct terms
from a given sequence of integers, Studia Sci. Math. Hung. 27
(1992),
173-182.
[26] - Distribution of solutions of diophantine equations f1(x1)f2(x2) = f3(x3) where fi are polynomials II, (con A. Schinzel),
Rend. Sem. Mat. Univ. Padova, 92 (1994), 29-46.
[27] - Some remarks on the S-unit equation in function fields, Acta
Arith. LXIV (1993), 87-98.
[28] - Ritt's second theorem in arbitrary characteristic, Journal
reine angew. Math., 445 (1993), 175-203.
[29] - Fields containing values of algebraic functions, (con
R. Dvornicich), Ann. Scuola Norm. Sup. Cl. Sci., XXI
(1994), 421-443.
[30] - A note on Thue's equation in function fields, (con R. Dvornicich),
Monatshefte fur Math., 118, 219-230 (1994)
[31] - The class semigroup of orders in number fields, (con P. Zanardo),
Math. Proc. Camb. Phil. Soc., 115 (1994), 379-391.
[32] - On Davenport's bound for the degree of f3 - g2 and Riemann
Existence
Theorem, Acta Arith., LXXI (1995), 107-137.
[33] - Note on the density constant in the distribution of self numbers,
(con G. Troi), Boll. U.M.I., (7) 9-A (1995), 143-148.
[34] - An effective solution of a certain diophantine problem,
Rend. Sem. Mat. Univ. Padova., 93 (1995), 177-183.
[35] - Fields containing values of algebraic functions II (On a conjecture of
Schinzel), (con R. Dvornicich), Acta Arith., XXII (1995),
201-210.
[36] - The least admissible value of the parameter in Hilbert's Irreducibility
Theorem (con A. Schinzel), Acta Arith., LXIX (1995), 293-302.
[37] - Commutative domains which are large in their M-adic completion,
(con P. Zanardo), Rend. Sem. Mat. Univ. Padova, 95 (1996), 1-9.
[38] - Algebraic points on subvarieties of Gmn, (con E.
Bombieri), International Math. Res. Notices, 7 (1995),
333-347.
[39] - Note on dense universal Hilbert sets, C. R. Acad. Sci. Paris,
322, Sèrie I, (1996), 703-706.
[40] - On periodic mod p sequences and G-functions (On a conjecture of
Ruzsa), Manuscripta math., 90 (1996), 391-402.
[41] - Appendix to the paper by M.Nair and A.Perelli: A sieve
fundamental lemma for polynomials in two variables, (con A.Schinzel),
Proc. of
the Halberstam Conference, Urbana, 1995.
[42] - Fields containing values of algebraic functions and related
questions, in: Number Theory 1993-94, S. David Ed., 199-213, Cambridge
Univ. Press 1996.
[43] - Remarks on a question of Skolem about the integer solutions of
x1x2-x3x4=1, Acta Arith., LXXVIII (1996), 153-164.
[44] - On the reduction modulo p of an absolutely irreducible polynomial
f(x,y), Arch. Math., 68 (1997) 129-138.
[45] - Vanishing sums of roots of unity, Rend. Sem. Mat. Univ. Pol.
Torino,
53, 4 (1995) 487-495.
[46] - Heights of Algebraic Points on Subvarieties of Abelian Varieties,
(con E. Bombieri), Ann. Scuola Norm Sup. Pisa Cl. Sci., (4)
XXIII. Fasc. 4 (1996)
[47] - On a Theorem of J.E. Olson and an Application - (Vanishing Sums in
Finite Abelian p-Groups, (con G. Troi), Finite Fields and Their
Applications, 3 (1997), 378-384.
[48] - Hilbert's irreducibility theorem and G-functions, (con P. Dèbes),
Math. Ann., 309 (1997), 491-503.
[49] - Arithmetic in Infinite Extensions of Function Fields, (con P.
Corvaja), Boll. U.M.I., (7) 11-B (1997), 1021-1038.
[50] - On a functional equation relating a Laurent series f(x) to f(xm),
Aequationes Math., 55 (1998), 15-43.
[51] - Values of rational functions on non-hilbertian fields and a
question of Weissauer, (con P. Corvaja), Israel Journal of
Mathematics, 105 (1998), 323-335.
[52] - Universal Hilbert Subsets, (con P. Dèbes), Math. Proc.
Camb. Phil. Soc. (1998), 124, 127-134.
[53] - On the number of times a root of f(n,x)=0 generates a field
containing a given number field, Journal of Number Theory, 72
(1998), 1-12.
[54] - Polynomials modulo p whose values are squares. (Elementary
improvements on some consequences of Weil's bounds.), L'Enseignement
Mathématique, 44 (1998), 95-102.
[55] - Note on g-hilbertian fields and nonrational functions with the
Hilbert property, Manuscripta Math. (1998), 155-162.
[56] - Two problems related to the non-vanishing of L(1,c) (con P.
Codecà
e R. Dvornicich), Journal de Théorie des Nombres de Bordeaux, 10
(1998), 49-64.
[57] - Diophantine equations with power sums and Universal Hilbert
Sets, (con P. Corvaja), Indag. Mathem., N.S., 9 (3) (1998),
317-332.
[58] - Appendix to the paper: Siegel's lemma, Padé approximations and
Jacobians, by E. Bombieri and P.B. Cohen, Ann. Scuola Norm.
Sup. Pisa Cl. Sci., (4) Vol.XXV (1997) 155-178.
[59] - Note on the density constant in the distribution of self numbers II,
(con G.Troi), Boll. U.M.I. (8) 2-B (1999), 397-399.
[60] - A note on traces of differential forms, Journal of Pure
Appl. Algebra, 142 (1999), 91-97.
[61] - Intersecting a Curve with Algebraic Subgroups of Multiplicative
Groups (con
E. Bombieri e D. Masser), International Mathematics Research Notices,
20 (1999), 1119-1140.
[62] - A Local-Global Principle for Norms from Cyclic Extensions of Q(t) (a
direct, constructive and quantitative approach), L'Einseignement
Mathématique, 45 (1999), 357-377.
[63] - On sums of Roots of Unity (con R. Dvornicich), Monatshefte für
Mathematik 129 (2000), 97-108.
[64] - A proof of Pisot dth root conjecture, Annals of
Mathematics,
151 (2000), 375-383.
[65] - Proof of Conjecture 1, (risultato ottenuto con E. Bombieri),
Appendix to the
book Polynomials with Special Regard to Reducibility by A. Schinzel,
Encyclopoedia of Pure and Applied Mathematics, vol. 77, Cambridge University
Press, 2000.
[66] - Multiplicative dependence and bounded height, an example, (con Paula B.
Cohen), in Algebraic Number Theory and Diophantine Analysis,
Proceedings of
the International Conference held in Graz, Austria, Aug. 30/ Sept. 5, 1998,
93-101.
[67] - On the diophantine equation f(am,y)=bn, (con P. Corvaja), Acta
Arith. 94.1 (2000), 25-40.
[68] - A relative Dobrowolski Lower Bound over Abelian Extensions, (con F.
Amoroso) Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) XXIX (2000),
711-727.
[69] - Fractional Parts of Linear Polynomials and an Application to
Hypergeometric
Functions, (con R. Dvornicich) J. Austral. Math. Soc. 70 (2001),
401-423.
[70] - Equations in one variable over function fields, (con E. Bombieri e J.
Mueller), Acta Arith. 99 (2001), 27-39.
[71] - Good reduction of certain covers ¶1 --> ¶1, Israel
J. of
Math., 124 (2001), 93-114.
[72] - Genus one curves defined by separated variable polynomials and a
polynomial
Pell equation (con R. Avanzi) Acta Arith. 99 (2001), 227-256.
[73] - A Note on heights in certain infinite extensions of Q (con E.
Bombieri), Rend. Mat. Acc. Lincei, s. 9, v. 12 (2001), 5-14.
[74] - Local-global divisibility of rational points in some commutative
algebraic groups (con R. Dvornicich), Bull. Soc. Math. France, 129
(2001), 317-338.
[75] - Fewnomials and intersections of lines with real analytic subgroups in
Gmn (con Paula B. Cohen), Bull. London Math. Soc. 34 (2002),
21-32.
[76] - A subspace theorem approach to integral points on curves (con P.
Corvaja),
C. R. Acad. Sci. Paris, Ser I 334 (2002), 267-271.
[77] - Some New Applications of the Subspace Theorem (con P. Corvaja),
Compositio Math. 131 (2002), 319-340.
[78] - Finiteness of integral values for the ratio of two linear
recurrences (con
P. Corvaja), Inventiones Math. 149 (2002), 431-451.
[79] - Sums of roots of unity vanishing modulo a prime (con. R.
Dvornicich),
Arch. Math. 79 (2002), 104-108.
[80] - A Note on squares in arithmetic progressions II (con E. Bombieri),
Rend. Mat. Acc. Lincei, s. 9, 13 (2002), 69-75.
[81] - An upper bound for the G.C.D. of an-1 and bn-1 (con Y.
Bugeaud e P.
Corvaja), Math. Zeit. 243 (2003), 79-84.
[82] - On polynomials taking small values at integral arguments II (con R.
Dvornicich e S.P. Tung), Acta Arith. 106 (2003), 115-121.
[83] - On the greatest prime factor of (ab+1)(ac+1) (con P. Corvaja),
Proc.
Amer. Math. Soc. 131 (2003), 1705-1709.
[84] - Parametrizing SL2(Z) and a question of Skolem, Acta
Arith.,
110 4 (2003), 331-337.
[85] - On the number of integral points on algebraic curves (con P.
Corvaja),
J. reine angew. Math. 565 (2003), 27-42.
[86] - The Equation f(X)=f(Y) in Rational Functions X=X(t), Y=Y(t)
(con R.
Avanzi), Compositio Math. 139 (2003), 263-295.
[87] - Solution of a problem about symmetric functions (con R. Dvornicich),
Rocky Mountain Journal of Mathematics, 33 (2003), 1279-1287.
[88] - Finiteness Results for Multiplicatively Dependent Points on Complex
Curves
(con E. Bombieri and D. Masser), Michigan Math. J. 51 (2003),
451-466.
[89] - On a Property of the Adele Ring of the rationals (con D. Dikranjan),
in
Rings, Modules, Algebras and Abelian Groups, A. Facchini, E. Houston, L.
Salce Eds.,
Proc. Algebra Conference, Venezia, LN in Pure Appl. Math., 236,
Marcel Dekker Inc., New Yors-Basel, 2004, 133-138.
[90] - An analogue for elliptic curves of the Grunwald-Wang example (con R.
Dvornicich), C. R. Acad. Sci. Paris, Ser. I 338 (2004), 47-50.
[91] - On the Number of Rational Points on certain Elliptic Curves (con E.
Bombieri), Izv. Ross. Akad. Nauk Ser. Mat. 68, 3 (2004), 5-14 (in
russo).
[92] - On a general Thue equation (con P. Corvaja), American Journal of
Math. 126 (2004), 1033-1055.
[93] - On integral points on Surfaces (con P. Corvaja), Annals of Math.
159 (2004).
Libri: Some Applications of Diophantine Approximation to Diophantine
Equations, 74 pp., Editrice Forum, Udine, Dicembre 2003.
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