Publications

1. M. Hajli -«Sur la fonction Zêa associéeau Laplacien singulier \Delta_O(m)\infty. Journal of Number Theory (2013), 71 pp, Volume 133, Issue 12, Pages 4069- 439, http://dx.doi.org/10.1016/j.jnt.2013.06.007. 

2. M. Hajli -«Volume arithmétique de certains fibrés hermitiens sur une variété torique lisse  Kyoto J. Math, 21 pp. (2014), no. 4, pp 819-840, doi:10.1215/21562261- 2801831. (3)  

3. M. Hajli -«Spectre du Laplacien singulier associé aux étriques canoniques sur la droite projective complexe et la théorie des séries de Fourier-Bessel généraliśee » Journal de Mathématiqu es Pures et appliquées.   41 pp. Volume  no. 2, pp 429-471. http://dx.doi. rg/10.1016/j.matpur.2014.04.010.     

4. M. Hajli torsion analytique holomorphe généralisée des fibrés en droites integrabes » Comptes rendus de l’Académie des Sciences, (2014), 5 pp. (2014), no. 5, pp 441-445. (5)  

5. M. Hajli -«On an arithmetic inequality on P1Q » International Journal of Number eory, (2014), 5 pp. (2015), no. 4, pp. 1227-1231. (6)  

6. M. Hajli -«On the invariant spectrum on the complex projective line. » Mathematihe Nachrichten (2015), 12 pp. (2015), no. 14-15, pp 1622-1633. (7)  

7. M. Hajli -« Hauteurs canoniques des sous-variétés toriques» Journal  of Number Theory , (2015), 40 pp, (2015), pp. 230-269. (8)  M.

8. M. Hajli  -« On the normalized arithmetic Hilbert function» Algebra and Number Theory, (2015), 12 pp, IF=0.8 9 (2015), no. 10, pp. 2293-2302.      

9. M. Hajli -« Growth of balls of holomorphic sections on projective toric varieties» International Journal of Mathematics (2016), 17 pp. Volume 27 (2016), no. 4, 1650028, 17 pp.                                                                                                                                                                "Let O(D) be an equivariant line bundle which is big and nef on a complex projective nonsingular toric variety X. Given a continuous toric metric ∥·∥ on O(D), we define the energy at equilibrium of (X,φD) where φD is the weight of the metrized toric divisor D = (D, ∥·∥). We show that this energy describes the asymptotic behavior as k goes to ∞ of the volume of the L2-norm unit ball induced by (X,kφD) on the space of global holomorphic sections H0(X, O(kD))."

10. M. Hajli -« On the arithmetic of translated monomial maps. » Funct. Approx. Comment. Math. (2018), 9 pp, Volume 58 (2018), no. 2, pp. 177-186.                                                                                                                                                                                           "Inspired by the work of Silverman on the geometry and the arithmetic of monomial maps and also on the translated maps on Abelian varieties, we generalize his results to the case of the translated monomial maps."

11. M. Hajli -« The canonical spectrum of projective toric manifolds. » Internat. J. Math. (2018), 18 pp, Volume 29 (2018), no. 7, 1850048, 18 pp.                                                                                                                                                                                                            "Let X be a complex projective toric manifold. We associated to X, a positive and closed (1,1)-current called the canonical toric Kahler current of X denoted by ωX,can, and a new invariant called the canonical spectrum of X. This spectrum is obtained as the set of the eigenvalues of a singular Laplacian defined by ωX,can and which is described uniquely by the combinatorial structure of X. The construction of this Laplacian and the study of its spectral properties are the consequence of a generalized spectral theory of Laplacians on compact Kahler manifolds that we develop in this paper"

12. M. Hajli -« A new formula for the Mahler measure.» Funct. Approx. Comment. Math. (2019), 6 pp, Volume 62 (2020), no. 2, pp.165-170.                                                                                                                                                                                                                    "Let f ∈ Z[x1, . . . , xN ] be a nonzero polynomial. We show that there exists a sequence of real numbers defined in terms of the coefficients of f, converging to the Mahler’s measure of f. This formula can be seen as a higher generalisation of Szego's limit formula".

13.  M. Hajli -« On the spectral zeta functions of the Laplacians on the projective complex spaces and on the n-spheres.»  Journal Number Theory(2019),28pp, Volume 16 (2020), no. 4, pp 693-717.                                                                                                                   "We present a powerful method for the calculation of heat- kernel coefficients of the Laplacian on the projective complex spaces endowed with the Fubini-Study metric, and also for the Laplacian on the n-spheres equipped with the standard metric. Formulas for the regularized determinants are also given".

14.  M. Hajli -« A generalized spectral theory for continuous metrics on compact Riemann surfaces.» J. Math. Anal. Appl. (2020), pp 26, Volume 481 (2020), no. 1, 123456, 26 pp.                                                                                                                                                                "We extend the spectral theory of generalized Laplacians to continuous metrics on compact Riemann surfaces. We define a holomorphic analytic torsion for any continuous metric. As an application of this theory, we partly recover some results of the theory of Bessel functions, for instance, Lommel’s theorem on the reality of the zeros of Bessel functions of order exceeding −1".

15.  M. Hajli -« The spectral properties of a continuous family of zeta functions.» International Journal of Number Theory (2020), 25 pp, Volume 16 (2020), no. 4, pp. 693-717.                                                                                                                                                      "In this article we study a family of zeta functions (Znl (s; a))l∈N  parametrized by a continuous variable a. When l = 0, Zn0(s;a) corresponds to the zeta function of a conformal Laplacian on the n-sphere.  We prove that Znl(s;a) is holomorphic at the origin, for l = 0,1,2,....We explicitly compute the values of ∂ Z 0 (s; a) and ∂ Z 1 (s; a), we show that these values are polynomials in a".

16.  M. Hajli; Bayad, A.  -« On the multidimensional zeta functions associated with theta functions,and the multidimensional Appell polynomials» Mathematical Methods in the Applied Sciences (2019), 16 pp, Volume 43(5), pp. 2679-2694.                                                                                                                                                                                                     "We define and study the multidimensional Appell polynomials associated with theta functions. For the trivial theta functions, we obtain the various well-known Appell polynomials. Many other interesting examples are given. To push our study, by Mellin transform, we introduce and investigate the multidimensional zeta functions associated with thetas functions and prove that the multidimen- sional Appell polynomials are special values at the nonpositive integers of these zeta functions. Using zeta functions techniques, among others, we prove an induction formula for multidimensional Appell polynomials."

17.  M. Hajli -« On a formula for the regularized determinant of zeta functions with application to some Dirichlet series» Quarterly Journal of Mathematics (2020), 23 pp, https://doi.org/10.1093/qmathj/haaa006.                                                                                           "We study a large class of zeta functions. We evaluate explicitly the special values of these zeta functions and the associated derivatives at 0. As an application, we recover several results on the zeta functions defined by two polynomials already obtained in the literature". 

18.  M. Hajli -« Sur une inégalité fonctionnelle sur les espaces projectifs»  Manuscripta Math.   (2020), 21 pp,                                                           "In this paper we introduce a new functional on the complex projective space defined on the set of invariant metrics on the line bundle O(1). We compare it to some classical functionals. As an application, we study the variation of the holomorphic analytic torsion".

19. M.Hajli, with S. Bouarroudj -« On the explicit formulas for zeta functions», Mathematical Methods in the Applied Sciences 

(2020).            "A large class of zeta functions that arises in geometric analysis and mathematical physics is studied. They are attached to some elliptic operators. This method can be used to evaluate explicitly the special values of zeta functions of elliptic operators defined on some symmetric spaces".

20. Hajli, Mounir,  "Sur une inégalité fonctionnelle sur les espaces projectifs avec applications à la torsion analytique holomorphe". Manuscripta Math. 165 (2021), no. 3-4, 483–503.

21. Hajli, Mounir, "Explicit computations of some spectral invariants of compact symmetric spaces of rank one", Mathematical Methods in the Applied Sciences (2022).

22. Bayad, Abdelmejid; Hajli, Mounir,  "The extended Eulerian numbers over function fields". Appl. Anal. Discrete Math. 16 (2022), 

23. Hajli, Mounir; ''The theta invariants and the volume function on arithmetic varieties''. Trans. Amer. Math. Soc. 376 (2023), 

24.  Hajli, Mounir; ''A new proof of some of Shintani's formulas'', Kyoto Journal of Mathematics; Volume 63 (3), 2023,

25.  Bayad, A.; Hajli, Mounir; ''On Jacobi forms and explicit evaluations of some trigonometric sums'', The Ramanujan Journal, Volume 60, 2023,

26. Hajli, Mounir, ''On the theory of Bott-Chern secondary characteristic classes with  applications to singular metrics'', Manuscripta Mathematica, (2023),

27. Hajli, Mounir,  "On the sum and the regularized products of some Dirichlet series",  The Ramanujan Journal, (2024).