Alessandro Languasco

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Alessandro Languasco

Research, Papers and Talks


Papers: List Papers; (with Abstracts); (with Citations). Curriculum (in Italian; long version ; short version). Google Scholar profile. ResearchGate page. Orcid ID. Scopus Author ID. Thomson Reuters Researcher ID.



Research Activities

Analytic Number Theory: with a particular interest on Riemann zeta-function and Dirichlet L-functions.
Additive Number Theory: with a particular interest on additive problems with primes.
Computational Number Theory: primality, factorization of integers.
Cryptography.


Papers, Preprints and Lecture Notes

The pdf files of the papers can be downloaded by clicking on their title or number. Many recent preprints of mine can also be downloaded from the arxiv website A. Languasco arxiv preprints or on my ResearchGate page. Note that preprints may differ from the published articles; hence, if you wish to cite a paper of mine, do not cite the arxiv file; please, if available, cite the final published version instead.

Preprints

[R54] A. Languasco, A. Zaccagnini - A Cesáro average for generalised Hardy-Littlewood numbers - in preparation.
[R53] A. Languasco, A. Zaccagnini - A Cesáro average for an additive problem with prime powers - in preparation.
[R52] A. Languasco, A. Zaccagnini - Short intervals asymptotic formulae for binary problems with prime powers - preprint 2016, submitted.

To Appear

[R51] A. Languasco, A. Zaccagnini - Cesáro average in short intervals for Goldbach numbers - to appear in Proc. A.M.S., 2017. Arxiv version

Published papers (in reverse chronological order)

[R50] A. Languasco, A. Zaccagnini - Il fascino discreto della Teoria dei Numeri - Sapere, gennaio-febbraio 2017, 22--26.
[R49] A. Languasco, A. Perelli, A. Zaccagnini - An extended pair-correlation conjecture and primes in short intervals - Trans. A.M.S. 369 (2017), 4235--4250.
[R48] A. Languasco, A. Zaccagnini - Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 - The Ramanujan Journal 42 (2017), 371--383. MR .
[R47] A. Languasco - Applications of some exponential sums on prime powers: a survey - Proceedings of the ``Terzo Incontro Italiano di Teoria dei Numeri", Scuola Normale Superiore, Pisa, 21-24 Settembre 2015. Rivista di Matematica della Università di Parma, volume 7, pages 19-37, 2016.
[R46] A. Languasco, A. Zaccagnini - Short intervals asymptotic formulae for binary problems with primes and powers, II: density 1 - Monatsh. Math. 181 (2016), 419--435. MR , ZBL .
[R45] A. Languasco, A. Perelli, A. Zaccagnini - An extension of the pair-correlation conjecture and applications - Mathematical Research Letters 23 (2016), 201-220. MR , ZBL .
[R44] A. Languasco, A. Zaccagnini - Sum of one prime and two squares of primes in short intervals - Journal of Number Theory 159 (2016), 1945--1960. MR , ZBL .
[R43] A. Languasco, A. Zaccagnini - A Diophantine problem with prime variables - In V. Kumar Murty, D. S. Ramana, and R. Thangadurai, editors, Highly Composite: Papers in Number Theory, Proceedings of the International Meeting on Number Theory, celebrating the 60th Birthday of Professor R. Balasubramanian (Allahabad, 2011), RMS-Lecture Notes Series, 2016, volume 23, pages 157-168.
[R42] A. Languasco, A. Zaccagnini - A Cesáro average of Goldbach numbers - Forum Mathematicum 27(4) 2015, 1945--1960. MR , ZBL .
[R41] A. Languasco, A. Zaccagnini - Explicit relations between primes in short intervals and exponential sums over primes - Functiones et Approximatio, Commentarii Mathematici 51 (2014), no. 2, 379--391. MR , ZBL .
[R40] A. Languasco, A. Zaccagnini - On a ternary Diophantine problem with mixed powers of primes - Acta Arithmetica 159 (2013), no. 4, 345--362. MR , ZBL .
[R39] A. Languasco, A. Zaccagnini - A Cesáro average of Hardy-Littlewood numbers - Journal of Mathematical Analysis and Applications, 401 (2013), no. 2, 568--577. MR , ZBL .
[R38] A. Languasco, A. Zaccagnini - A Diophantine problem with a prime and three squares of primes - Journal of Number Theory. 132 (2012), no. 12, 3016--3028. MR , ZBL .
[R37] A. Languasco, V. Settimi - On a Diophantine problem with one prime, two squares of primes and s powers of two - Acta Arithmetica, 154 (2012), 385--412, Computational part. MR , ZBL .
[R36] A. Languasco, A. Perelli, A. Zaccagnini - Explicit relations between pair correlation of zeros and primes in short intervals - Journal of Mathematical Analysis and Applications, 394 (2012), 761--771. MR , ZBL .
[R35] A. Languasco, A. Zaccagnini - Sums of many primes - Journal of Number Theory, 132 (2012), no. 6, 1265--1283. MR , ZBL .
[R34] A. Languasco, A. Zaccagnini - The number of Goldbach representations of an integer - Proc. A.M.S., 140 (2012), no. 3, 795--804. MR , ZBL .
[R33] A. Languasco, A. Zaccagnini - Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions - with an Appendix by Karl. K. Norton - Experimental Mathematics, 19.3 (2010), 279--284, Computational part. Some computational results (with few digits) are also listed at the bottom of the arxiv preprint: see arxiv.org/abs/0906.2132 . MR , ZBL .
[R32] A. Languasco, A. Zaccagnini - On a Diophantine problem with two primes and s powers of two - Acta Arithmetica 145 (2010), 193--208, Computational part. MR , ZBL .
[R31] A. Languasco, A. Perelli, A. Zaccagnini - On the Montgomery-Hooley theorem in short intervals - Mathematika 56 (2010), 231--243. MR , ZBL .
[R30] A. Languasco, A. Zaccagnini - On the constant in the Mertens formula for arithmetic progressions. I. Identities - Functiones et Approximatio, Commentarii Mathematici, 42 (2010), 17--27. MR , ZBL .
[R29] D. Bazzanella, A. Languasco, A. Zaccagnini - Prime numbers in logarithmic intervals - Transactions of the American Mathematical Society, 362 (2010), 2667-2684. MR , ZBL .
[R28] A. Languasco - A conditional result on the exceptional set for Hardy-Littlewood numbers in short intervals - International Journal of Number Theory, 5 (2009), 933--951. MR , ZBL .
[R27] A. Languasco, A. Zaccagnini - On the constant in the Mertens formula for arithmetic progressions. II. Numerical values - Math. Comp. 78 (2009), 315-326. Computational part. MR , ZBL .
[R26] A. Languasco, A. Zaccagnini - On the Hardy-Littlewood problem in short intervals - International Journal of Number Theory, 4 (2008), 715--723. MR , ZBL .
[R25] A. Languasco, A. Zaccagnini - Some estimates for the average of the error term of the Mertens product for arithmetic progressions - Functiones et Approximatio, Commentarii Mathematici, 38 (2008), 41--48. MR , ZBL .
[R24] A. Languasco, J. Pintz, A. Zaccagnini - On the sum of two primes and k powers of two - Bulletin of the London Mathematical Society, 39 (2007), 771--780. MR , ZBL .
[R23] A. Languasco, A. Zaccagnini - A note on Mertens' formula for arithmetic progressions - Journal of Number Theory 127 (2007), 37-46. MR , ZBL .
[R22] A. Languasco, A. Zaccagnini - Intervalli tra numeri primi consecutivi - Disponibile in rete presso il sito web Bocconi, 2005.
[R21] A. Languasco, A. Zaccagnini - Esistono piccoli intervalli tra numeri primi consecutivi ! - Disponibile in rete presso il sito web Bocconi, 2005.
[R20] A. Languasco - On the sum of a prime and a k-free number - Functiones et Approximatio, Commentarii Mathematici, 34 (2005), 19-26. MR , ZBL .
[R19] A. Languasco, A. Zaccagnini - Alcune proprietà dei numeri primi, II - Disponibile in rete presso il sito web Bocconi, 2005.
[R18] A. Languasco - The exceptional set in short intervals for two additive problems with primes:  a survey in the Proceedings of the ``Secondo Incontro Italiano di Teoria dei Numeri'', Parma 2003, Italy, ed. by A. Zaccagnini et al, Riv. Mat. Univ. Parma 7 , (2004), 223-231. MR , ZBL .
[R17] A. Languasco, A. Zaccagnini - Alcune proprietà dei numeri primi, I - Disponibile in rete presso il sito web Bocconi, 2005.

[R16] A. Languasco - On the exceptional set for Hardy-Littlewood's numbers in short intervals - Tsukuba Journal of Mathematics, 28 (2004) 169-192. MR , ZBL .
[R16]-Corrigendum A. Languasco - Corrigendum to: On the exceptional set for Hardy-Littlewood's numbers in short intervals - Tsukuba Journal of Mathematics, 30 (2006), 237--240. MR , ZBL .

[R15] A. Languasco - On the exceptional set of Goldbach numbers in short intervals - Monatshefte für Mathematik 141 (2004), 147-169. MR , ZBL .

[R14] A. Languasco, F. Menegazzo, M. Morigi - On the composition length of finite primitive linear groups - Arch. Math. 79 (2002), 408-417. MR , ZBL .

[R13] A. Languasco, A. Perelli - Crittografia e firma digitale - in "Matematica e Cultura: Arte, tecnologia e immagini", Bologna 2000, ed. da M.Emmer e M.Manaresi, Springer Verlag Italia, 2002, 99-106, (Italian). The english [R13eng] translation is published in ``Mathematics, Art, Technology, and Cinema'', Springer Verlag, 2003.

[R12] J. Kaczorowski, A. Languasco, A. Perelli - A note on Landau's formula - Functiones et Approximatio 28 (2000), 173-186. MR , ZBL .

[R11] A. Languasco - An introduction to Cryptography - in "The Curves Seminar at Queen's", vol. 13, ed. by A.V. Geramita, Queen's Papers in Pure and Applied Mathematics, volume 119, (2000), 121-140.

[R10] A. Languasco, A. Perelli - Pair correlation of zeros, primes in short intervals and exponential sums over primes - Journal of Number Theory, 84 (2000), 292-304. MR , ZBL .

[R9] D. Bazzanella, A. Languasco - On the asymptotic formula for Goldbach numbes in short intervals - Studia Sci. Math. Hungar, 36 (2000), 185-199. MR , ZBL .

[R8] A. Languasco, A. Perelli - Numeri primi e Crittografia - in "Matematica e Cultura 2000", Venice 1999, ed. by M.Emmer, Springer Verlag Italia, 2000, 227-233, (Italian). The english [R8eng] translation is published in ``Mathematics and Culture I'', Springer Verlag, 2003.

[R7] A. Languasco - Some refinements of error terms estimates for certain additive problems with primes - J. Number Theory, 81 (2000), 149-161. MR , ZBL .

[R6] A. Languasco - A note on primes and Goldbach numbers in short intervals - Acta Math. Hungar., 79 (1998), 191-206. MR , ZBL .

[R5] A. Languasco - A singular series average and Goldbach numbers in short intervals - Acta Arith., 83 (1998), 171-179. MR , ZBL .

[R4] A. Languasco - A conditional result on Goldbach numbers in short intervals - Acta Arith., 83 (1998), 93-103. MR , ZBL .

[R3] A. Languasco, A. Perelli - A pair correlation hypothesis and the exceptional set in Goldbach's problem - Mathematika 43 (1996), 349--361. MR , ZBL .

[R2] A. Languasco - Some results on Goldbach's problem - Proceedings of "Incontro Italiano di Teoria dei Numeri", Terza Università di Roma, 1995; Rend. Sem. Mat. Univ. Pol. Torino, 53 (1995), 325--337. MR , ZBL .

[R1] A. Languasco, A. Perelli - On Linnik's theorem on Goldbach Numbers in short intervals and related problems - Ann. Inst. Fourier, 44 (1994), 307--322. MR , ZBL .


Dissertations

[D1] A. Languasco - Public Key Codes and Primality Tests - M. Sc. Dissertation (1989) (Italian).

[D2] A. Languasco - The Goldbach Conjecture - Ph.D. Thesis (1995) (Italian).


Lecture Notes

[LN1] A. Languasco - Dispense di Analisi Matematica Uno - Manuscript (1999) (Italian).
[LN2] A. Languasco - Dispense di Algebra Lineare, Geometria e Calcolo Differenziale in più variabil - Manuscript (2001) (Italian). Revised version for the academic year 2002-2003.
[LN3] B. Bruno, A. Languasco - Dispense integrative per il Corso di Istituzioni di Analisi Matematica II - 2003 (Italian).
[LN4] A. Languasco - Dispense di Metodi Matematici per la Statistica - 2004 (Italian).



Talks

[1] ''Comologia di Cech'', per il corso di Algebra Commutativa (Prof. P.Valabrega) del Dottorato di Ricerca del consorzio UniTo, PoliTo, UniGe, 1991.
[2] ''Analisi non-standard'' per il corso di Logica Matematica (Prof. G.Lolli) del Dottorato di Ricerca del consorzio UniTo, PoliTo, UniGe, 1991.
[3] ''Il teorema di Bombieri-Vinogradov e sue estensioni, I, II, III'', Università di Genova, 1993.
[4] ''Crivello pesato e Teorema di Chen, I,II'', Università di Genova, 1994.
[5] ''Alcuni risultati sulla congettura di Goldbach'', Incontro Italiano di Teoria dei Numeri, Terza Università di Roma, 1995.
[6] ''Una (breve) introduzione alla crittografia'', Associazione Mathesis, Università di Padova, 1998.
[7] ''Approssimazione diofantea e algoritmo LLL, I,II,III'', Università di Padova, 2001.
[8] ''Sull'insieme eccezionale in intervalli corti di due problemi additivi con numeri primi'', Secondo Incontro Italiano di Teoria dei Numeri, Università di Parma, 2003.
[9] ''Piccole differenze tra primi consecutivi (dopo Goldston, Motohashi, Pintz, Yildirim)'' Università di Genova, 08.06.2005.
[10] ''Lauree Scientifiche: Pari/GP e la crittografia.'' Congresso OpenMath 2005, Università di Padova, sede di Vicenza, 14.12.2005.
[11] ''On the sum of a prime and a k-free number'', Italian-Polish Number Theory Days, Poznan (Poland), 18.05.2006. Poster
[12] ''Numeri primi e Crittografia'', Università di Modena, 04.10.2006.
[13] ''On the sum of a two primes and k powers of two'', Genova, 15.05.2007, Parma 18.05.2007, Edinburgh (Journees Arithmetiques 2007) 02.07.2007.
[14] ''Alcuni Attacchi a RSA'', Ferrara, 23.05.2007.
[15] ''On the constant in the Mertens product for arithmetic progressions: Numerical values'', Analytic Number Theory Workshop, Parma, Italy, 15-16.05.2008.
[16] ''Sul problema di Goldbach-Linnik'', La Teoria dei Numeri, Università di Roma Tre, Roma, Italy, 27-29.05.2009. Poster
[17] ''On the Montgomery-Hooley formula in short intervals'', International Italy-India Conference on Diophantine and Analytic Number Theory, Scuola Normale Superiore, Pisa (Italy), 11.03.2010.
[18] ``On the average number of Goldbach representation of an integer'', Analytic and Combinatorial Number Theory, ICM satellite conference, Institute of Mathematical Sciences, Chennai (India), 29.08.2010.
[19] ``On the average number of Goldbach representation of an integer'', Number Theory and its applications, An international Conference dedicated to Kálmán Győry, Attila Pethő, János Pintz, András Sárközy, Institute of Mathematics University of Debrecen, Hungary, October 4-8, 2010.
[20] ``Una formula esplicita per i numeri di Goldbach'', XIX Congresso UMI, Universita' di Bologna, 15 Settembre 2011.
[21] ``RSA: firma digitale e attacchi'', Progetto CAM, Universita' di Padova, 28 Novembre 2014.
[22] "On some exponential sums over prime powers and applications", Settembre 2015: Terzo Incontro Italiano di Teoria dei Numeri, Scuola Normale Superiore, Pisa (Italy).
[23] ``Diophantine problems with primes'', Dipartimento di Matematica e Informatica dell'Università di Parma, 30/05, 31/05, 01/06/2016. Poster.
[24] ``Formule esplicite per problemi additivi con numeri primi'', Workshop di Teoria dei Numeri, Dipartimento di Matematica, Universit\`a di Torino, Novembre 2016, (invited speaker).



Ultimo aggiornamento: 14.03.2017: 19:24:08

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