Contacts

giocop {at} interfree .it

Giovanni Coppola

Analytic Number Theory Researcher

 

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
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 -> giovanni coppola number theory(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 -> giovanni coppola number theory(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 – Universit& 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 – Universit& 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/1312.5701v1- 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 PDF: Download Publication 1 (see Nat.Conf.Proceedings) 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 PDF: Download Publication 2 (see Italian Journals) Download Publication 2 (see Italian Journals)
MR 98k:11118, Pub.n.2 (see pdf)
Download PDF: Download Abstract 1 (see Italian Journals) Download Abstract 1 (see Italian Journals)
MR 2005f:11209, Abstract 1 (see pdf)
Given Talks

(SEE Conferences Page)

• ‘Distribuzione asintotica dei numeri primi in intervalli corti’ at the Math.Department ‘Renato Caccioppoli’, University of Neaples ‘Federico II’(ITALY),18 April 1997
• ‘ON THE DISTRIBUTION IN THE ARITHMETIC PROGRESSIONS OF REDUCIBLE QUADRATIC POLYNOMIALS IN SHORT INTERVALS, I-II’ within the (quoted) ‘Journées Arithmétiques, XXI’, Roma, 12 July 1999
• ‘SYMMETRY OF ARITHMETICAL FUNCTIONS OVER SHORT INTERVALS’ in the (quoted) ‘Première Journées du Nord sur les nombres premiers’, Lille, 28 June 2001
• ‘ON THE SYMMETRY OF THE DIVISOR FUNCTION IN ALMOST ALL SHORT INTERVALS’ within the (quoted) ‘Journées Arithmétiques, XXII’, Lille, 5 July 2001
• ‘SIMMETRIA DI FUNZIONI ARITMETICHE IN QUASI TUTTI GLI INTERVALLI CORTI’ in the (quoted) ‘Second Italian Number Theory Meeting’, Parma, 2003 on the 13th November 2003 (Download PDF below)
• ‘ON THE SYMMETRY OF SOME CLASSES OF ARITHMETICAL FUNCTIONS IN SHORT INTERVALS’ in the (quoted) ‘Journées Arithmétiques, XXIV’, Marseille, on the 8th July 2005 (Download PDF below)
• ‘Crivello Largo e Simmetria in Intervalli Corti’ given (at DIMA, Department of Mathematics) in the University of Genova, Genova-ITALY, on the 19th September 2006 (Download PDF below)
• ‘ON THE SELBERG INTEGRAL OF THE k-DIVISOR FUNCTION AND THE 2k-TH MOMENT OF THE RIEMANN ZETA FUNCTION’ in the quoted ‘Journées Arithmétiques, XXVI’, St. Etienne, on the 8th July 2009 (Download PDF below).
• ‘'On some lower bounds of some symmetry integrals' in the quoted 'Italy-India Conference on Diophantine and Analytic Number Theory, Centro De Giorgi, 8th-14th March 2010, Pisa (Italy)'.
• ‘‘Aspetti elementari del metodo della Dispersione e del Crivello Largo’, during the (quoted) ‘XIX Congresso UMI’ on the 15 September 2011, Bologna, Italy.  (Download PDF below).
• “CAPARIS - Combinatoire Additive à Paris”, Institut Henri Poincaré, Paris; Paris, France, 9-13 July 2012
• “ELAZ - ELEMENTARE UND ANALYTISCHE ZAHLENTHEORIE (ELEMENTARY AND ANALYTIC NUMBER THEORY)”, at Schloß Schney, Institut für Mathematik, Julius- Maximilians- Universität Würzburg; Würzburg, Germany, 13-18 August 2012
• “SAVANT - Synergies And Vistas in Analytic Number Theory”, Conference in Honour of Roger Heath-Brown, Mathematical Institute, Oxford; Oxford,United Kingdom, 3-7 September 2012
• “Journées Arithmétiques, XXVIII”, Université de Grenoble I,CNRS - Institut Fourier, St-Martin d'Hères Cedex, Grenoble; Grenoble, France, 1-5 July 2013  (Download PDF below).