Pubblicazioni

1. M. Cantarini, On the Cesàro average of the «Linnik's numbers», Acta Arithmetica 180 (1) (2017), 45-62.

2. M. Cantarini, On the Cesàro average of the numbers that can be written as sum of a prime and two squares of primes, Journal of Number Theory 185 (2018), 194-217.

3. M. Cantarini, J. D'Aurizio, On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums, J. Boll. Unione Mat. Ital. 12 (4) (2019), 623-656.

4. M. Cantarini, Explicit formula for the average of Goldbach numbers, Indian Journal of Mathematics 61 (2019), 253-279.

5. M. Cantarini, Some identities involving the Cesàro average of Goldbach numbers, Mathematical Notes 106 (5) (2019), 688-702.

6. M. Cantarini, A. Gambini, A. Zaccagnini, On the average number of representations of an integer as a sum of like prime powers, Proc. Amer. Math. Soc. 148 (4) (2020), 1499–1508.

7. M. Cantarini, A. Gambini, A. Languasco, A. Zaccagnini, On an average ternary problem with prime powers, The Ramanujan Journal 53 (1) (2020), 155-166.

8. M. Cantarini, A. Gambini, A. Zaccagnini, A note on an average additive problem with prime numbers, Funct. Approx. Comment. Math., 63 (2) (2020), 215-226.

9. M. Cantarini, D. Costarelli, G. Vinti, A solution of the problem of inverse approximation for the sampling Kantorovich operators in case of Lipschitz functions, Dolomites Research Notes on Approximation, 13 (2020), 30-35.

10. M. Cantarini, D. Costarelli, G. Vinti, Asymptotic expansion for neural network operators of the Kantorovich type and high order of approximation, Mediterr. J. Math. 18, 66 (2021). 

11. M. Cantarini, A. Gambini, A. Zaccagnini, Cesàro averages for Goldbach representations with summands in arithmetic progressions, International Journal of Number Theory, 17 (10) (2021), 2379-2393.

12. M. Cantarini, A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series, The Ramanujan Journal, 59 (2) (2022), 549–557.

13. J. M. Campbell, M. Cantarini, J. D'Aurizio, Symbolic computations via Fourier-Legenre expansions and fractional operators, Integral Transforms and Special Functions, 33 (2) (2022), 157–175.

14. M. Cantarini, D. Costarelli, G. Vinti, Approximation of differentiable and not differentiable signals by the first derivative of sampling Kantorovich operators, Journal of Mathematical Analysis and Applications, 509 (1), 125913 (2022).

15. M. Cantarini, L. Coroianu, D. Costarelli, S. G. Gal, G. Vinti, Inverse result of approximation for the max-product neural network operators of the Kantorovich type and their saturation order, Mathematics, 10 (1) (2022), 63.

16. J. M. Campbell, M. Cantarini, A series evaluation technique based on a modified Abel lemma, Turkish Journal of Mathematics, 46 (4) (2022), 1520-1537.

17. M. Cantarini, C. Marcelli, F. Papalini, Wavefront solutions for a class of nonlinear highly degenerate parabolic equations, Journal of Differential Equations, 332 (2022), 278–305.

18. M. Cantarini, A. Gambini, A. Zaccagnini, A Cesàro average for an additive problem with an arbitrary number of prime powers and squares, Research in Number Theory, 8 (3) (2022), 50. 

19. M. Cantarini, D. Costarelli, G. Vinti, Convergence of a Class of Generalized Sampling Kantorovich Operators Perturbed by Multiplicative Noise. In: Candela, A.M., Cappelletti Montano, M., Mangino, E. (eds) Recent Advances in Mathematical Analysis. Trends in Mathematics. Birkhäuser, Cham. (2023). 

20. M. Cantarini, D. Costarelli, G. Vinti, Approximation results in Sobolev and fractional Sobolev spaces by Sampling Kantorovich Operators, Fractional Calculus and Applied Analysis, 26 (6) (2023), 2493–2521. 

21. M. Cantarini, Correction to: On the interplay between hypergeometric series, Fourier–Legendre expansions and Euler sums (Bollettino dell'Unione Matematica Italiana, (2019), 12, 4, (623-656), 10.1007/s40574-019-00198-5), Bollettino dell'Unione Matematica Italiana, 17 (1) (2024), 175.

22. M. Cantarini, Hypergeometric series, lemniscate functions, q-extensions and Jacobi elliptic functions, Note di Matematica 44 (2) (2024), 1–16.

23. M. Cantarini, C. Marcelli, F. Papalini, Wavefront solutions for reaction-diffusion-convection models with accumulation term and aggregative movements, Nonlinear Differ. Equ. Appl. 32 (2), article n. 23 (2025). 

24. M. Cantarini, A. Gambini, A. Zaccagnini, Laplace convolutions of weighted averages of arithmetical functions, Forum Mathematicum 37 (2) (2025), 515–533. 

25. M. Cantarini, D. Costarelli, Simultaneous approximation by neural network operators with applications to Voronovskaja formulas, Mathematische Nachrichten 298 (3) (2025), 871–885.

26. M. Cantarini, D. Costarelli, An application of the Euler-MacLaurin summation formula for estimating the order of approximation of sampling-type series, Dolomites Research Notes on Approximation, 18 (2) (2025), 1–7.

27. M. Cantarini, Connection formulas between Fourier-Legendre/Jacobi expansions and central binomial series, Integral Transforms and Special Functions 36 (11) (2025), 940–960.

28. M. Cantarini, D. Costarelli, Multivariate Neural Network operators: simultaneous approximation and Voronovskaja-type theorem, Mathematical Methods in the Applied Sciences 48 (2) (2025), 10669–10677.

29. M. Cantarini, A. Gambini, A. Zaccagnini, On the discrete convolution of the Liouville and M\"obius functions, submitted.

30. M. Cantarini, G. Vinti, Approximation properties of Sampling Kantorovich operators in Besov, Triebel-Lizorkin and fractional Sobolev spaces, submitted.

31. M. Cantarini, Averages of diagonal Elliott-Halberstam problem twisted by M\"obius function with Sobolev and H\"older-Zygmund weights, submitted.