Research Interests
My interests of research
My research interests belong to Analytic Number Theory.
In particular, I study the distribution of arithmetic functions in short intervals and/or in the arithmetic progressions, by Sieve Methods, Dispersion Method and Kloosterman sums estimates.
I miei interessi di ricerca si trovano nell’ambito della Teoria Analitica dei Numeri.
In particolare, problemi di distribuzione di funzioni aritmetiche in intervalli corti e/o nelle progressioni aritmetiche, tramite i metodi di crivello, della dispersione e di stime di somme di Kloosterman.
Online Papers
Online Papers:
Publications in National Conferences Proceedings
G.Coppola, M.B.S.Laporta - "ON THE REPRESENTATION OF EVEN INTEGERS AS SUM OF TWO ALMOST EQUAL PRIMES" - Number theory, I (Rome, 1995). Rend. Sem. Mat. Univ. Politec. Torino 53 (1995), no. 3, 245--252. MR 98h:11122
Publications in International Conferences Proceedings
G.Coppola, S.Salerno - "ON THE DISTRIBUTION IN THE ARITHMETIC PROGRESSIONS OF QUADRATIC REDUCIBLE POLYNOMIALS IN SHORT INTERVALS, II" - 21st Journées Arithmétiques (Rome, 2001). J. Théor. Nombres Bordeaux 13 (2001), no. 1, 93--102. MR 2002e:11126
Italian Journals
G.Coppola, M.B.S.Laporta - "A NEW "WEIGHTED" FORM OF THE RIEMANN-VON MANGOLDT EXPLICIT FORMULA" - Note Mat. 14 (1994), no. 2, 263--275 (1997). MR 98k:11118
G.Coppola - "ON THE SYMMETRY OF PRIMES IN ALMOST ALL SHORT INTERVALS" - Ricerche Mat. 52 (2003), no. 1, 21—29. MR 2005f:11209
G.Coppola - "ON THE SYMMETRY OF SQUARE-FREE NUMBERS IN ALMOST ALL SHORT INTERVALS" – Riv. Mat. Univ. Parma (Serie 7) 3* (2004), 205-212. MR 2005k:11192
International Journals
G.Coppola, A.Vitolo - "ON THE DISTRIBUTION OF PRIMES IN INTERVALS OF LENGTH $logsp heta N$" - Acta Math. Hungar. 70 (1996), no. 1-2, 151--166. MR 96i:11103
G.Coppola, A.Vitolo - Corrigendum to: " ON THE DISTRIBUTION OF PRIMES IN INTERVALS OF LENGTH $logsp heta N$" [Acta Math. Hungar. 70 (1996), no. 1-2, 151--166; MR 96i:11103]. Acta Math. Hungar. 78 (1998), no. 4, 359--361. MR 99c:11115
G.Coppola, S.Salerno - "ON THE DISTRIBUTION IN THE ARITHMETIC
PROGRESSIONS OF QUADRATIC REDUCIBLE POLYNOMIALS IN SHORT INTERVALS" - Dedicated to Wl odzimierz Sta's on the occasion of his 75th birthday. Funct. Approx. Comment. Math. 28 (2000), 75--81. MR 2002a:11111
PROGRESSIONS OF QUADRATIC REDUCIBLE POLYNOMIALS IN SHORT INTERVALS" - Dedicated to Wl odzimierz Sta's on the occasion of his 75th birthday. Funct. Approx. Comment. Math. 28 (2000), 75--81. MR 2002a:11111
S.D.Adhikari, G.Coppola - "ON THE AVERAGE OF THE SUM-OF-ODD-DIVISORS FUNCTION" - Currents trends in number theory (Allahabad, 2000), 1--15, Hindustan Book Agency, New Delhi, 2002. MR 2003f:11143
S.D.Adhikari, G.Coppola, A.Mukhopadhyay - "ON THE AVERAGE OF THE SUM -OF-THE-$p$-PRIME-DIVISORS FUNCTION" - Acta Arith. 101 (2002), no. 4, 333--338. MR 2002k:11163
G.Coppola - "ON THE SYMMETRY OF DIVISOR SUMS FUNCTIONS IN ALMOST ALL SHORT INTERVALS" - Integers 4 (2004), A2, 9 pp. (electronic). MR 2005b:11153 -> 
(download pdf version)
(download pdf version)G.Coppola, S.Salerno - "ON THE SYMMETRY OF THE DIVISOR FUNCTION IN ALMOST ALL SHORT INTERVALS" - Acta Arith. 113 (2004), no. 2, 189—201. MR 2005a:11144
G.Coppola - "ON THE SYMMETRY OF SQUARE-FREE SUPPORTED ARITHMETICAL FUNCTIONS IN ALMOST ALL SHORT INTERVALS" – J. of Inequalities in Pure and Applied Math. 5 (2004), no. 2, Article 33 (electronic). MR 2005f:11210 -> (download pdf version)
(download pdf version)G.Coppola, S.Salerno - "ON THE SYMMETRY OF ARITHMETICAL FUNCTIONS IN ALMOST ALL SHORT INTERVALS" – C. R. Math. Rep. Acad. Sci. Canada 26 (2004), no. 4, 118—125. MR 2005m:11180
G. Coppola - "On the Selberg integral of the $k$-divisor function and the $2k$-th moment of the Riemann zeta function" - Publ. Inst. Math. (Beograd) (N.S.) 88(102) (2010), 99--110. MR 2011m:11173
G. Coppola - "On the correlations, Selberg integral and symmetry of sieve functions in short intervals" - http://arxiv.org/abs/0709.3648v3 - 9 pp. (electr.) - Extended version on Journal of Combinatorics and Number Theory 2.2 (2010), 91-105.
G. Coppola - "On the correlations, Selberg integral and symmetry of sieve functions in short intervals, II" - Int. J. Pure Appl. Math. 58 (2010), no. 3, 281--298. MR2640394
G. Coppola - "ON SOME LOWER BOUNDS OF SOME SYMMETRY INTEGRALS" - http://arxiv.org/abs/1003.4553v2 - 10 pp. (electr.) - Extended version "Afr. Mat. 25 issue 1 (2014), 183–195" (Springer Verlag).
G. Coppola and M. Laporta - "GENERATIONS OF CORRELATION AVERAGES" - Journal of Numbers Volume 2014 (2014), Article ID 140840, 13 pages http://dx.doi.org/10.1155/2014/140840
G. Coppola and M. Laporta - "A generalization of Gallagher's lemma for exponential sums" - To appear on Siauliai Mathematical Seminar
Preprints
G. Coppola, M.B.S. Laporta - "ALMOST EQUAL PRIME SOLUTIONS OF LINEAR EQUATIONS IN TWO VARIABLES" - Preprint - University of Salerno, 1999;
G. Coppola, S. Salerno - "ON THE DISTRIBUTION IN THE ARITHMETIC PROGRESSIONS OF QUADRATIC REDUCIBLE POLYNOMIALS IN SHORT INTERVALS, III" - Preprint;
G. Coppola - "ON THE SYMMETRY OF DISTRIBUTION OF THE PRIME-DIVISORS FUNCTION IN ALMOST ALL SHORT INTERVALS" - Preprint (to appear);
G. Coppola, H. Iwaniec - "ON THE SYMMETRY OF HECKE EIGENVALUES OF MODULAR FORMS IN ALMOST ALL SHORT INTERVALS" – Preprint n. 19 – Luglio 2005 – Università di Salerno;
G. Coppola - "ON THE SYMMETRY OF ARITHMETICAL FUNCTIONS IN ALMOST ALL SHORT INTERVALS, II" – Preprint n. 13 – Luglio 2006 – Università di Salerno;
Coppola - "ON THE SYMMETRY OF ARITHMETICAL FUNCTIONS IN ALMOST ALL SHORT INTERVALS, III" – Preprint n. 14 – Luglio 2006 – Università di Salerno.
Online Papers
G. Coppola - "ON THE MODIFIED SELBERG INTEGRAL" - available online at http://arxiv.org/abs/1006.1229v1 - 6 pp. (electronic).
G. Coppola - "ON THE SYMMETRY INTEGRAL" - available online at http://arxiv.org/abs/1007.1018v1 - 5 pp. (electronic).
G. Coppola - "ON THE CORRELATIONS, SELBERG INTEGRAL AND SYMMETRY OF SIEVE FUNCTIONS IN SHORT INTERVALS, III" - available at http://arxiv.org/abs/1003.0302v1 - 11 pp. (electronic).
G. Coppola - "ON THE SELBERG INTEGRAL OF THE THREE-DIVISOR FUNCTION d3" - available at http://arxiv.org/abs/1207.0902v3 - 4 pp. (electronic).
G. Coppola and M. Laporta - "A MODIFIED GALLAGHER'S LEMMA" - available at http://arxiv.org/abs/1301.0008v1 - 19 pp. (electronic).
G. Coppola and M. Laporta - "SYMMETRY AND SHORT INTERVAL MEAN-SQUARES" - available at http://arxiv.org/abs/1312.5701v3- 19 pp. (electronic).
G. Coppola and M. Laporta - "A generalization of Gallagher’s lemma for exponential sums"- available at http://arxiv.org/abs/1411.1739v1 - 14pp.(electronic).
Collaborating with the scientific reviews:
- Reviewer for “Mathematical Reviews”
- Reviewer for “Zentralblatt MATH”
Avellino, 31st. January, 2015
Download Publication 1 (see Nat.Conf.Proceedings)
MR 98h:11122, Pub.n.1 (see pdf)
Coppola, G.; Laporta, M. B. S. "On the representation of even integers as sum of two almost equal primes. Number theory, I (Rome, 1995)."
Download Publication 2 (see Italian Journals)
MR 98k:11118, Pub.n.2 (see pdf)
Download Abstract 1 (see Italian Journals)
MR 2005f:11209, Abstract 1 (see pdf)