Many recent preprints of mine can also be downloaded from the arxiv website A. Languasco arxiv preprints arxiv preprints or on my ResearchGate page. Preprints may differ from the published articles and are not considered by the scientometric counters; if you wish to cite a paper of mine, please cite the final published version.

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Preprints

1. N. Khandil, A. Languasco, P. Moree - Pair Correlation of zeros of Dirichlet L-Functions: A path towards the Montgomery and Elliott-Halberstam Conjectures - submitted, 2024. MR , ZBL .
2. S. Al Haj-Baddar, A. Languasco, M. Migliardi - Fast and accurate implementation of the Dirichlet multinomial log-likelihood function - preprint 2024, submitted.
3. N. Khandil, A. Languasco, P. Moree, S. Saad Eddin, A. Sedunova - Relative class numbers and Euler--Kronecker constants of maximal real cyclotomic subfields - preprint, 2024, submitted. Computational part. MR , ZBL .
4. A. Languasco, F. Luca, P. Moree, A.Togbé - Sequences of integers generated by two fixed primes - submitted, 2023. Computational part. CodeOcean capsule.
5. A. Languasco, P. Moree - Quadratic residue bias of the divisor function and Fekete polynomials - preprint 2022, submitted. MR , ZBL .
6. A. Languasco, P. Moree, S. Saad Eddin, A. Sedunova - Computation of the Kummer ratio of the class number for prime cyclotomic fields - Arxiv 2019.

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Published papers (in reverse chronological order)

7. N. Khandil, A. Languasco, P. Moree - The Brauer-Siegel ratio for prime cyclotomic fields - to appear in Pacific Journal of Mathematics, 2025. MR , ZBL .
8. A. Languasco, P. Moree - Euler constants from primes in arithmetic progression - to appear in Mathematics of Computation, 2025. Computational part, Code Ocean capsule.
9. S. Al Haj-Baddar, A. Languasco, M. Migliardi - Modeling and forecasting overdispersed IoT data using an efficient and accurate computation of the Dirichlet Multinomial distribution - accepted for the 2025 Workshop on Computing, Networking and Communications (CNC), Honolulu, Hawaii, February 17-20, 2025.
10. S. Al Haj-Baddar, A. Languasco, M. Migliardi - Efficient analysis of overdispersed data using an accurate computation of the Dirichlet multinomial distribution - IEEE Transactions on Pattern Analysis and Machine Intelligence, 47 (2):1181-1189, 2025. CodeOcean capsule.
11. N. Khandil, A. Languasco, P. Moree, S. Saad Eddin, A. Sedunova - The Kummer ratio of the relative class number for prime cyclotomic fields - J. Math. Anal. Appl. 538(1):Paper No. 128368, 2024. Computational part. MR , ZBL .
12. A. Languasco - A partially Decentralised Protocol for a Distributed Encrypted Storage system - In Jose Bravo and Gabriel Urzaiz, editors, Proceedings of the 15th International Conference on Ubiquitous Computing & Ambient Intelligence (UCAmI 2023), pages 195--204, Cham, 2023. Springer Nature Switzerland
13. A. Languasco - Numerical estimates on the Landau-Siegel zero and other related quantities - J. Number Theory 251 (2023), 185--209. Computational part. MR , ZBL .
14. A. Languasco, M. Migliardi - On the fast computation of the Dirichlet-multinomial log-likelihood function - Comput. Stat. 38 (2023), 1995-2013. MR , ZBL .
15. Y. Lamzouri, A. Languasco - Small values of | L'/L (1, χ) | - Exp. Math. 32 (2023), 362--377. Computational part. MR , ZBL .
16. A. Languasco - A unified strategy to compute some special functions of number-theoretic interest - J. Number Theory 247 (2023), 118--161. Computational part. MR , ZBL .
17. A. Ciolan, A. Languasco, P. Moree - Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms - J. Math. Anal. Appl., 519 (2023), 1--48, paper n. 126854 Computational part , CodeOcean capsule. MR , ZBL .
18. A. Languasco - On computing L'/L(1,χ) - Rend. Semin. Mat. Univ. Politec. Torino 80 (2022), 55--71. Proceeding of the 5th Number Theory Meeting, Università and Politecnico of Torino, October 26-27th, 2021. MR , ZBL .
19. A. Languasco, T.S. Trudgian - Uniform effective estimates for | L (1, χ) | - J. Number Theory 236 (2022), 245--260. Computational part. MR , ZBL .
20. A. Languasco, L. Righi - A fast algorithm to compute the Ramanujan-Deninger Gamma function and some number-theoretic applications - Math. Comp. 90 (2021), 2899--2921. Computational part. MR , ZBL .
21. A. Languasco, A. Zaccagnini - Sum of one prime power and two squares of primes in short intervals - Rocky Mountain J. Math. 51 (2021), 213--224. MR , ZBL .
22. A. Languasco - Numerical verification of Littlewood's bounds for |L(1,χ)| - J. Number Theory 223 (2021), 12--34. Computational part, Code Ocean capsule. MR , ZBL .
23. A. Languasco - Efficient computation of the Euler-Kronecker constants for prime cyclotomic fields - Res. Number Theory 7 (2021), no. 1, Paper No. 2, Computational part, MR , ZBL .
24. A. Languasco, A. Zaccagnini - Short intervals asymptotic formulae for binary problems with prime powers, II - J. Aust. Math. Soc. 109 (2020), 351--370. MR , ZBL .
25. M. Cantarini, A. Gambini, A. Languasco, A. Zaccagnini - On an average ternary problem with prime powers - Ramanujan J. 53 (2020), 155--166. MR , ZBL .
26. A. Languasco, A. Zaccagnini - Sums of four prime cubes in short intervals - Acta Math. Hung. 159 (2019), 150--163. MR , ZBL .
27. A. Languasco, A. Zaccagnini - A Cesáro average for generalised Hardy-Littlewood numbers - Kodai Math. J. 42 (2019), 358--375. MR , ZBL .
28. A. Languasco, A. Zaccagnini - A Cesáro average for an additive problem with prime powers - Proceedings of the conference “Number Theory Week”, Poznań, September 4–8, 2017. Banach Center Publications, Institute of Matehematics, Polish Academy of Sciences, Warszawa, volume 118, 2019, pp. 137--152. MR , ZBL .
29. A. Languasco, A. Zaccagnini - Short intervals asymptotic formulae for binary problems with prime powers - J. Théor. Nombres Bordeaux 30 (2018), 609--635. MR , ZBL .
30. A. Gambini, A. Languasco, A. Zaccagnini - A Diophantine approximation problem with two primes and one k-power of a prime - J. Number Theory 188 (2018), 210--228. MR , ZBL .
31. A. Languasco, A. Zaccagnini - Il fascino discreto della Teoria dei Numeri - Sapere, gennaio-febbraio 2017, 22--26.
32. A. Languasco, A. Zaccagnini - Cesáro average in short intervals for Goldbach numbers - Proc. Amer. Math. Soc. 145 (2017), 4175--4186. MR , ZBL .
33. A. Languasco, A. Perelli, A. Zaccagnini - An extended pair-correlation conjecture and primes in short intervals - Trans. Amer. Math. Soc. 369 (2017), 4235--4250. MR , ZBL .
34. A. Languasco, A. Zaccagnini - Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 - Ramanujan J. 42 (2017), 371--383. MR , ZBL .
35. 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. MR , ZBL .
36. 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 .
37. A. Languasco, A. Perelli, A. Zaccagnini - An extension of the pair-correlation conjecture and applications - Math. Res. Lett. 23 (2016), 201-220. MR , ZBL .
38. A. Languasco, A. Zaccagnini - Sum of one prime and two squares of primes in short intervals - J. Number Theory 159 (2016), 1945--1960. MR , ZBL .
39. 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. MR .
40. A. Languasco, A. Zaccagnini - A Cesáro average of Goldbach numbers - Forum Math. 27(4) 2015, 1945--1960. MR , ZBL .
41. A. Languasco - Numeri primi - Chapter 11 of the volume "Numeri tutto quello che conta, da zero a infinito", by C. Bartocci and L. Civalleri, pages 183-193, 2014. Codice Edizioni, Torino.
42. A. Languasco, A. Zaccagnini - Explicit relations between primes in short intervals and exponential sums over primes - Funct. Approx. Comment. Math. 51 (2014), no. 2, 379--391. MR , ZBL .
43. A. Languasco, A. Zaccagnini - On a ternary Diophantine problem with mixed powers of primes - Acta Arith. 159 (2013), no. 4, 345--362. MR , ZBL .
44. A. Languasco, A. Zaccagnini - A Cesáro average of Hardy-Littlewood numbers - J. Math. Anal. Appl. 401 (2013), no. 2, 568--577. MR , ZBL .
45. A. Languasco, A. Zaccagnini - A Diophantine problem with a prime and three squares of primes - J. Number Theory 132 (2012), no. 12, 3016--3028. MR , ZBL .
46. A. Languasco, V. Settimi - On a Diophantine problem with one prime, two squares of primes and s powers of two - Acta Arith. 154 (2012), 385--412, Computational part, CodeOcean capsule. MR , ZBL .
47. A. Languasco, A. Perelli, A. Zaccagnini - Explicit relations between pair correlation of zeros and primes in short intervals - J. Math. Anal. Appl. 394 (2012), 761--771. MR , ZBL .
48. A. Languasco, A. Zaccagnini - Sums of many primes - J. Number Theory 132 (2012), no. 6, 1265--1283. MR , ZBL .
49. A. Languasco, A. Zaccagnini - The number of Goldbach representations of an integer - Proc. Amer. Math. Soc. 140 (2012), no. 3, 795--804. MR , ZBL .
50. A. Languasco, A. Zaccagnini - Computing the Mertens and Meissel-Mertens constants for sums over arithmetic progressions - with an Appendix by Karl. K. Norton - Exp. Math. 19.3 (2010), 279--284, Computational part, CodeOcean capsule #1 , CodeOcean capsule #2. Some computational results (with few digits) are also listed at the bottom of the arxiv preprint: see arxiv.org/abs/0906.2132 . MR , ZBL .
51. A. Languasco, A. Zaccagnini - On a Diophantine problem with two primes and s powers of two - Acta Arith. 145 (2010), 193--208, Computational part. MR , ZBL .
52. A. Languasco, A. Perelli, A. Zaccagnini - On the Montgomery-Hooley theorem in short intervals - Mathematika 56 (2010), 231--243. MR , ZBL .
53. A. Languasco, A. Zaccagnini - On the constant in the Mertens formula for arithmetic progressions. I. Identities - Funct. Approx. Comment. Math. 42 (2010), 17--27. MR , ZBL .
54. D. Bazzanella, A. Languasco, A. Zaccagnini - Prime numbers in logarithmic intervals - Trans. Am. Math. Soc., 362 (2010), 2667-2684. MR , ZBL .
55. A. Languasco - A conditional result on the exceptional set for Hardy-Littlewood numbers in short intervals - Int. J. Number Theory 5 (2009), 933--951. MR , ZBL .
56. 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, CodeOcean capsule. MR , ZBL .
57. A. Languasco, A. Zaccagnini - On the Hardy-Littlewood problem in short intervals - Int. J. Number Theory 4 (2008), 715--723. MR , ZBL .
58. A. Languasco, A. Zaccagnini - Some estimates for the average of the error term of the Mertens product for arithmetic progressions - Funct. Approx. Comment. Math. 38 (2008), 41--48. MR , ZBL .
59. A. Languasco, J. Pintz, A. Zaccagnini - On the sum of two primes and k powers of two - Bull. London Math. Soc. 39 (2007), 771--780. MR , ZBL .
60. A. Languasco, A. Zaccagnini - A note on Mertens' formula for arithmetic progressions - J. Number Theory 127 (2007), 37--46. MR , ZBL .
61. A. Languasco - Primos Gemelos - La Voz de Almeria, Seccion Matematica, 2005. (pubblicato il 04/09/2005 in lingua spagnola, traduzione di Juan Cuadra Diaz).
62. A. Languasco - On the sum of a prime and a k-free number - Funct. Approx. Comment. Math. 34 (2005), 19--26. MR , ZBL .
63. 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 .
64. A. Languasco - On the exceptional set for Hardy-Littlewood's numbers in short intervals - Tsukuba J. Math. 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 J. Math. 30 (2006), 237--240. MR , ZBL .

65. A. Languasco - On the exceptional set of Goldbach numbers in short intervals - Monatsh. Math. 141 (2004), 147--169. MR , ZBL .

66. 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.
67. A. Languasco, F. Menegazzo, M. Morigi - On the composition length of finite primitive linear groups - Arch. Math. 79 (2002), 408--417. MR , ZBL .

68. 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.

69. J. Kaczorowski, A. Languasco, A. Perelli - A note on Landau's formula - Funct. Approx. Comment. Math. 28 (2000), 173--186. MR , ZBL .
70. 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.

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

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

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

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

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

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

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

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

79. 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 .

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Articoli divulgativi (Papers on the popularisation of mathematics; in Italian)

[W4] A. Languasco, A. Zaccagnini - Intervalli tra numeri primi consecutivi - Disponibile in rete presso il sito web Bocconi, 2005.

[W3] A. Languasco, A. Zaccagnini - Esistono piccoli intervalli tra numeri primi consecutivi ! - Disponibile in rete presso il sito web Bocconi, 2005.

[W2] A. Languasco, A. Zaccagnini - Alcune proprietà dei numeri primi, II - Disponibile in rete presso il sito web Bocconi, 2005.

[W1] A. Languasco, A. Zaccagnini - Alcune proprietà dei numeri primi, I - Disponibile in rete presso il sito web Bocconi, 2005.

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Dissertations (in Italian)

[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).

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Lecture Notes (in Italian)

[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).

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Ultimo aggiornamento: 17.01.2025: 20:01:30