Welcome

I'm a Full Professor at the Department of Mathematics of the University of Genova, working in Analytic Number Theory.

Publications

  1. On products of sets of natural density one (with M. Bordignon, A. Fazzari). To appear in Math. Proc. Cambridge Philos. Soc. [Link to arXiv]
  2. A lower bound for the number of Egyptian fractions (with L. Grenié, G. Molteni, C. Sanna). Mathematics of Computation. [Link to published version]
  3. On quantum modular forms of non-zero weights (with S. Drappeau). Compositio Mathematica, Volume 161 , Issue 11 , November 2025 , pp. 3044 – 3087. [Link to published version]
  4. A weighted one-level density of the non-trivial zeros of the Riemann zeta-function (with A. Fazzari). Math. Z. 307(2), 32, 2024. [Link to published version]
  5. On the typical rank of rational elliptic surfaces (with F. Battistoni, C. Delaunay). Research in Number Theory, Volume 8, Article 69 (11 pp.), 2022. [Link to published version]
  6. Ranks of elliptic curves over Q(T) of small degree in T (with F. Battistoni, C. Delaunay). Preprint. [Link to arXiv]
  7. Limit laws for rational continued fractions and value distribution of quantum modular forms (with S. Drappeau). Proc. Lond. Math. Soc. (PLMS), Volume 125 (6), December 2022, 1377-1425. [Link to published version]
  8. Modularity and value distribution of quantum invariants of hyperbolic knots (with S. Drappeau). Math. Annalen 382, 2022, 1631–1679. [Link to published version]
  9. A note on the natural density of product sets (with D. Koukoulopoulos and C. Sanna). Bull. Lond. Math. Soc. (BLMS), Volume 53 (5), October 2021, 1407-141. [Link to published version]
  10. Effective estimation of some oscillatory integrals related to infinitely divisible distributions (with S. Drappeau). The Ramanujan Journal, 57, 849–861 (2022) [Link to published version]
  11. A quadratic divisor problem and moments of the Riemann zeta-function (with H.M. Bui, X. Li and M. Radziwill). Journal of the European Mathematical Society (JEMS), 2020, 22(12), pp. 3953–3980. [Link to published version]
  12. Averages of long Dirichlet polynomials (with J. B. Conrey). Riv. Mat. Univ. Parma, Vol. 12, No. 1, 2021, 1-27. [Link to published version]
  13. Two arithmetic applications of perturbations of composition operators (with S. Drappeau). Journal d'Analyse Mathematique, Volume 144, 335–349 (2021). [Link to published version]
  14. Greedy approximations by signed harmonic sums and the Thue-Morse sequence (with G. Molteni and C. Sanna). Advances in Mathematics, Volume 366, 3 June 2020, 107068 (42 pp.). [Link to published version]
  15. Mixed moments of characteristic polynomials of random unitary matrices (with E.C. Bailey, G. Blower, J.B. Conrey, A. Prokhorov, M.O. Rubinstein, N.C. Snaith). Journal of Mathematical Physics 60, 083509 (26 pp.), 2019. [Link to published version]
  16. Partial sums of the cotangent function (with S. Drappeau). Journal de Théorie des Nombres de Bordeaux, 32 (2020) no. 1, pp. 217-230. [Link to published version]
  17. The power-saving Manin-Peyre's conjectures for a senary cubic (with K. Destagnol). Mathematika, volume 65 (2019), issue 04, pp. 789-830. [Link to published version]
  18. A note on the dimension of the largest Hecke-submodule (with C. Perret-Gentil and M. Radziwill). Int. Math. Res. Not. IMRN, Volume 2021, Issue 7, April 2021, pp. 4907–4919. [Link to published version]
  19. Small values of signed harmonic sums (with G. Molteni and C. Sanna). C. R. Acad. Sci. Paris, Ser. I., 2018. Volume 356, Issues 11–12, 1062-1074. [Link to published version]
  20. High moments of the Estermann function. Algebra & Number Theory, Vol. 13 (2019), No. 2, 251–300. [Link to published version]
  21. Linear correlations of the divisor function. Acta Arithmetica 188 (2019) , 1-52. [Link to published version]
  22. Statistical distribution of the Stern sequence (with S. Drappeau and L. Spiegelhofer). Comment. Math. Helv. 94 (2019), no. 2, 241–271. [Link to published version]
  23. Non-isotrivial elliptic surfaces with non-zero average root number (with C. David and C. Delaunay). Journal Number Theory, Volume 191, October 2018, Pages 1-84.[Link to published version]
  24. Trilinear forms with Kloosterman fractions (with V. Chandee). Advances in Mathematics, 2018, vol. 328, p. 1234-1262. [Link to published version]
  25. A conjectural extension of Hecke's converse theorem (with J.W. Bober, A.R. Booker, B. Conrey, Min Lee, G. Molteni, T. Oliver, D.J. Platt and R.S. Steiner). The Ramanujan Journal, 2018, Volume 47, Issue 3, pp 659–684.[Link to published version]
  26. On the non-vanishing of certain Dirichlet series (with B. Martin). Journal of Number Theory, Volume 180, November 2017, Pages 423-442.[Link to published version]
  27. A congruence sum. Rend. Circ. Mat. Palermo, II. Ser., 66(3), 477-483 [Link to published version]
  28. The first moment of twisted Hecke L-functions with unbounded shifts. Funct. Approx. Comment. Math. Volume 57, Number 1 (2017), 105-114.[Link to published version]
  29. The θ=∞ conjecture implies the Riemann hypothesis (with S.M. Gonek). Mathematika, volume 63 (2017), issue 01, pp. 29-33. [Link to published version]
  30. On the reciprocity law for the twisted second moment of Dirichlet L-functions. Trans. Amer. Math. Soc. 368 (2016), 6887-6914. [Link to published version]
  31. On the distribution of a cotangent sum. Int Math Res Notices (2015) 2015 (21): 11419-11432. [Link to published version]
  32. The mean square of the product of the Riemann zeta function with Dirichlet polynomials (with V. Chandee and M. Radziwill). J. Reine Angew. Math. (Crelle) 729 (2017), 51–79. [Link to published version]
  33. A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials (with S.A. Altug, I. Petrow, Rishikesh and I. Whitehead). Quarterly Journal of Mathematics (2014) 65 (4): 1111-1125. [Link to published version]
  34. The second weighted moment of zeta (with J.B. Conrey). 6. Publications Mathématiques de Besançon - Algèbre et Théorie des Nombres (2013), 41-47. [Link to published version]
  35. A generalization of Rademacher's reciprocity formula. Acta Arith. 159 (2013), 363-374. [Link to published version]
  36. An optimal choice of Dirichlet polynomials for the Nyman-Beurling criterion (with J.B. Conrey and D.W. Farmer). Proceedings of the Steklov Institute of Mathematics. April 2013, Volume 280, Issue 2 Supplement (in honor of A.A. Karatsuba), pp 30-36. [Link to published version]
  37. Period functions and cotangent sums (with J.B. Conrey). Algebra & Number Theory 7 (2013), no. 1, 215-242. [Link to published version]
  38. A reciprocity formula for a cotangent sum (with J.B. Conrey). Int. Math. Res. Not. IMRN, 2013, no. 24, 5709-5726. [Link to published version]
  39. The second moment of the Riemann zeta function with unbounded shifts. Int. J. Number Theory 6 (2010), no. 8, 1933-1944. [Link to published version]

Ph.D. Thesis

  1. Moments, Period Functions and Cotangent Sums. Thesis (Ph.D.) - University of Bristol, 2010.