Directeur de Recherche Emérite C.N.R.S.
Institut de Recherche Mathématique Avancée
Unité Mixte de Recherche CNRS-UdS.
Coordonnées :
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Tél. : 03 68 85 01 76
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E-mail : michel.weber@unistra.fr
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Bureau : IRMA Emérites.
Articles récents.
(Publications : 160)
1. M. Weber, A Fourier analysis of quadratic Riemann sums and local integrals of the Riemann zeta-function, Abhandlungen aus der Mathematischen Seminar der Universität Hamburg, (2024), à paraître.
2. M. Weber, A uniform semi-local limit theorem along sets of multiples for sums of i.i.d. square integrable random variables, Funct. Approx. Comment. Math. 70 (2), 177--199 (2024).
3. M. Weber, Decoupling inequalities and decoupling coefficients of Gaussian processes, Sankhya A 86, 661--698 (2024).
4. M. Weber, On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem, Forum Math. 36, No. 1, 1--4 (2024).
5. M. Weber, Critical probabilistic characteristics of the Cramér model for primes and arithmetical properties, (27 p.), arXiv:2105.11020v1, Indian J. of Pure and Applied Math., (2024), à paraître.
6. M. Weber, Composed quadratic Riemann sums related to the Riemann Zeta function, (2024), en révision.
7. Z. Szewczak and M. Weber, Classical and almost sure local limit theorems, arXiv:2208.02700, Dissertationes Math., No 589, 1--97 (2023).
8. M. Weber, A strenghtened asymptotic uniform distribution, Probab. Math. Stat. 43, No. 2, 263--285 (2023).
9. S. Shi and M. Weber, On Jordan double sums and related summatory functions, Unif. Distrib. Theory 18 no. 2, 57--76, (2023).
10. M. Weber, On infinite Mobius inversion, Publ. Math. Debr. 103, No. 1-2, 1--12 (2023).
11. S. Shi and M. Weber, On the equation n_1 n_2 ...n_{k+1}=n_{k+2} ... , n_{2(k+1)} (9 p.), Integers, à paraître, (2023).
12. M. Weber, On Farey sequence and quadratic Farey sums, (25 p.), (2022) Research in Number Theory, 8, Article number 14, (22 p.).
13. R. Nair, J.-L. Verger-Gaugry and M. Weber, On good universality and the Riemann Hypothesis, (30 p.), (2021), Advances in Math., 385, 107762.
14. M. Weber, An extension of a result of Erdös-Zaremba, (2021) Glasgow Math. J., 63 (1), 193-222.
15. S. Shi, M. Weber, On the equation n_1n_2=n_3n_4 restricted to factor closed sets, (2018), Acta Math. Sinica, 34 (10), 1517-1530.
16. C. Cuny, M. Weber, On Nörlund summation and Ergodic Theory, with applications to power series of Hilbert contractions, (2018), Bull. Polish Acad. Sci., 66 No1, 69-85.
17. R. Giuliano, Z. Szewczak, M. Weber, Almost sure local limit theorem for the Dickman distribution, (2018), Periodica Math. Hung., 76 (2), 155-197.
18. C. Cuny, M. Weber, Pointwise convergence of almost periodic Fourier series and associated series of dilates, (2018), Pacific J. Math., 292 No. 1, 81--101.
19. C. Cuny, M. Weber, Ergodic theorems with arithmetical weights, (2017), Israel J. Math., 217, 139--180.
20. R. Giuliano, M. Weber. Approximate Local Limit Theorems with Effective Rate and Applications to Random Walks in Random Scenery, Bernoulli 23 (4B), (2017), 3268--3310.
21. P. Lertchoosakul, A. Jassova, R. Nair, M. Weber, Distribution functions for subsequences of generalized van der Corput sequences, (2017), Uniform Distribution Th., 12 no. 2, 1-10.
22. A. Basse-O'Connor, M. Weber, On the Phi-variation of stochastic processes with exponential moments, (2016), Trans. London Math. Soc. 3(1) 1--27.
23. M. Weber, Cauchy Means of Dirichlet Polynomials, J. Approx. Th., 216 (2016), 61--79.
24. M. Weber, An arithmetical approach to the convergence problem of series of dilated functions and its connection with the Riemann Zeta function, J. Number Th., 162 (2016), 137--179.
25. M. Weber, L1-Norms of Steinhaus Chaos on the Polydisc, (2016), Monath. Math. 181 no. 2, (2016), 473--483.
26. M. Weber. On convergence almost everywhere of series of dilated functions, C.R. Acad. Sci. Paris Ser. I, 353 (2015), 883-886.
27. M. Weber, Criteria of divergence almost everywhere in ergodic theory, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 441, (2015), Veroyatnost' i Statistika. 22, 73--118; translation in J. Math. Sci. (N.Y.) 219 no 5, (2016), 651--682.
28. R. Giuliano, M. Weber. Local limit theorems in some random models from Number theory, (2016), Stoch. Analysis. Appl. 34, no. 6, 941--960.
29. C. Aistleitner, I. Berkes, K. Seip, M. Weber, Convergence of series of dilated functions and spectral norms of GCD matrices, Acta Arithmetica 168.3 (2015), 221--246.
30. I. Berkes, M. Weber, On series sum c_kf(kx) and Khintchin's conjecture, Israel J. of Math. 201 no. 2 (2014), 593--609.
31. M. Weber, Local suprema of Dirichlet polynomials and zerofree regions of the Riemann zeta-function, Glasgow Math. J. 56, (2014), 643--655.
32. I. Berkes, M. Weber, On series of dilated functions, Quartely J. Math 65, no. 1, (2014), 25–52.
33. M. Weber, A bound for mean values of Fourier transforms, Math. Inequal. Appl. 17 no. 1, (2014), 83--94.
34. M. Weber, On small deviations of stationary Gaussian processes and related analytic inequalities, Sankhya A, 75 (2), (2013), 139--170.
35. M. Weber, On instants of small amplitude of the Ornstein-Uhlenbeck process with an application to the Kubilius model, Periodica Hungarica Math, 67 (1), (2013), 95--113.
36. M. Weber, On small deviations of Gaussian processes using majorizing measures, Colloquium Math. 129 (1) (2012), 41-59.
37. I. Berkes, W. Muller, M. Weber, A general strong law of large numbers for arithmetic functions, Indagationes Math. 23, (2012), 547-555.
38. M. Weber, On systems of dilated functions, C.R. Acad. Sci. Paris Ser. I, 349 (2011), 1261-1263.
39. M. Weber, A sharp correlation inequality with an application to almost sure local limit theorem, Prob. and Math. Stat. 31 (1) (2011), 79-98.
40. I. Berkes, W. Muller, M. Weber, On the strong law of large numbers and arithmetic additive functions, (2011), Periodica Math. Hung. 62 (1), 1-12.
41. M. Weber, On the zeros and local infima of Brownian motion, Comm. in Stoch. Analysis 5 (1) (2011), 1-13.
42. M. Weber, On mean values of Dirichlet polynomials, Math. Ineq. & Appl. 14 (3) (2011), 529-534.
43. M. Weber, Mean values estimates related to the Lindelöf hypothesis, Lithuanian J. Math. 51 (3) (2011), 82-105.
44. R. Giuliano, M. Weber, Almost sure local limit theorems with rate, Stochastic Analysis and Applications 29 (2011), 779--798.
45. M. Weber, A remark on the LIL for subsequences, Lobachevskii J. Math. 31 (4) (2010), 336.
46. M. Weber, Dirichlet polynomials: some old and recent results, and their interplay in number theory, (2010), Dependence in probability, analysis and number theory, 323--353, Kendrick Press, Heber City, UT.
47. M. Weber, Supremum of Random Dirichlet Polynomials with Submultiplicative Coefficients, Uniform Distribution Theory 5 (1) (2010), 163-197.
48. I. Berkes, S. Hormann, M. Weber, Upper-lower class tests for weighted i.i.d. sequences and martingales, J. Theoret. Probab. 23 (2) (2010), 428--446.
49. M. Weber, Dynamical Systems and Processes, European Mathematical Society Publishing House, IRMA Lectures in Mathematics and Theoretical Physics 14, (2009), xiii+759p.
50. M. Lifshits, M. Weber, Sampling the Lindelöf Hypothesis with the Cauchy random walk, Proc. London Math. Soc. 98 (3), (2009), 241-270.
51. I. Berkes, M. Weber, On the convergence $\sum_k c_k f(n_kx)$, Memoirs of the A.M.S. 201 no 943, (2009), vi+72p.
52. M. Lifshits, M. Weber, On the supremum of some Random Dirichlet polynomials, Acta Math. Hungar. 123 (1-2), (2009), 41--64.
53. M. Weber, On an identity of Ky Fan, Anal. Math. 34 (3), (2008), 225--236
54. M. Lin, M. Weber, Laws of the iterated logarithm for weighted sums of i.i.d. random variables, Comtemporary Math. 485, (2008), 115-129.
55. R. Giuliano-Antonini, M. Weber, The Theta dependence coefficient and almost sure limit theorems, Stat and Prob. Letters 78 (5), (2008), 564-575.
56. M. Lifshits, M. Weber, On the supremum of random Dirichlet polynomials, Studia Math. 182 (1), (2007), 41-65.
Prépublications.
1. M. Weber, On the Fourier inversion formula, (2024).
2. M. Weber, Divisibility and primality in random walks, (53 p.), arXiv:2310.14828v2 (2024).
4. M. Weber, A general correlation inequality for level sets of sums of independent random variables using the Bernoulli part with applications to the almost sure local limit theorem, (48 p.), arXiv:2305.19372v1, (2023).
5. S. Shi and M. Weber, Value distribution of squarefree divisors of Bernoulli sums, (15 p.), (2022).
6. M. Weber, Distribution and Correlation Properties of Divisors of the Bernoulli random walk, (68 p.), (2023).
7. M. Weber, On the number of solutions of the congruence equation y^2+ky = 0 (mod D), (6 p.), (2020).
Thèmes de recherches.
Théorie ergodique. Théorie des probabilités. Théorie des processus stochastiques. Théorie des séries orthogonales. Analyse spectrale. Sommes trigonométriques et sommes de Dirichlet. Fonction Zeta de Riemann. Fonctions arithmétiques. Théorie analytique et théorie probabiliste des nombres.Publications : Liste complète :
Séminaire.
Systèmes Dynamiques et Processus (1990/2003)Directions de thèses.
-- M. Atlagh, McF à l'Université de Strasbourg. (Thèse : Théorème central limite presque sur et loi du logarithme itéré, Juin 1993).
-- D. Schneider, Pr, l'Université du Littoral, Calais. (Thèse : "Convergence presque sure de moyennes ergodiques perturbées par des variables aléatoires", Juin 1994).
-- C. Gamet, (secteur privé). (Thèse : "Théorèmes de convergence en moyenne et entropie métrique de moyennes ergodiques", Novembre 1996).
-- J.J. Ruch, McF, Université de Bordeaux-I. (Thèse : "Contribution à l'étude des sommes de Riemann", Novembre 1997).
-- S. Kristensen, Université de Aarhus. (Thèse : "Sur deux formes d'approximation, Mars 2002).
-- F. Boukhari. Université de Tlemcen. (Thèse : "Convergence et propriétés métriques des moyennes ergodiques pondérées, Décembre 2002).
Dernières modifications : le 16 10 2024.
