Papers and Preprints

The pdf files for the preprints of  the new articles and of some of those already published can be downloaded by clicking on the title or on the number of the paper. Please note that the preprint may differ from the published article: existing laws forbid (I think) to modify preprints after the transfer of copyright. If you are interested in a reprint of  the article, please contact me here: languasco AT math.unipd.it (replace AT by @).

Papers. Papers and Abstracts. Curriculum (in Italian).

Monographs

[M1] A. Languasco, A. Zaccagnini - Introduzione alla Crittografia - Ulrico Hoepli Editore, 2004 (Italian). Online Review -- Errata

[M2] A. Languasco, A. Zaccagnini - Crittografia - Progetto Lauree Scientifiche per il Veneto, ed. CLEUP, Padova, 2006. Errata

Preprints

[P1] A. Languasco, A. Zaccagnini - A Diophantine problem with a prime and three squares of primes - preprint, 2012, submitted.

[P2] A. Languasco, A. Zaccagnini - L2-norm of exponential sums over prime powers - preprint, 2012, submitted.

[P3] A. Languasco, A. Perelli, A. Zaccagnini - Explicit relations between pair correlation of zeros and primes in short intervals - preprint, 2012, submitted.

[P4] A. Languasco, A. Zaccagnini - A Diophantine problem with prime variables preprint, 2012, submitted .

To Appear

[R36] A. Languasco, A. Zaccagnini - Sums of many primes - to appear in Journal of Number Theory, 2012.

[R35] A. Languasco, V. Settimi - On a Diophantine problem with one prime, two squares of primes and s powers of two - preprint, 2011, to appear in Acta Arithmetica. Computational part.

Published papers

[R34] A. Languasco, A. Zaccagnini - The number of Goldbach representations of an integer - Proc. A.M.S., 140 (2012), no. 3, 795--804.

[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

[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.

[R31] A. Languasco, A. Perelli, A. Zaccagnini - On the Montgomery-Hooley theorem in short intervals - Mathematika 56 (2010), 231--243.

[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.

[R29] D. Bazzanella, A. Languasco, A. Zaccagnini - Prime numbers in logarithmic intervals - Transactions of the American Mathematical Society, 362 (2010), 2667-2684.

[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.

[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.

[R26] A. Languasco, A. Zaccagnini - On the Hardy-Littlewood problem in short intervals - International Journal of Number Theory, 4 (2008), 715--723.

[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.

[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.

[R23] A. Languasco, A. Zaccagnini - A note on Mertens' formula for arithmetic progressions - Journal of Number Theory 127 (2007), 37-46.

[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.

[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.

[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.
[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.

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

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

[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.

[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.

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

[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.

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

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

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

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

[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.

[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.

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).