Abdelmejid BAYAD

The focus of my research lies at the intersection of algebraic and analytic number theory, algebraic and arithmetic geometry, graph theory, complex analysis,Fourier analysis, and applications to cryptography. Particular attention is given to the arithmetic of modular forms and the study of special values of L-functions and zeta functions.

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• S. Atmani; A. Bayad; D. Kim. Eisenstein series and partition functions. (submitted).
  

• A. Bayad; N. Kilar; Y. Simsek. A new look on Stirling numbers, Bernoulli and Euler type polynomials. (Submitted)
  

• A. Bayad; N. Kilar; Y. Simsek. Finite sums involving trigonometric functions and special polynomials: Analysis of generating functions and p-adic integrals. Appl. Anal. Discrete Math. 18 (2024), 452–476.
  

• A. Bayad; A. Raouj.Reciprocity laws for Dedekind cotangent sums. Rocky Mountain J. Math. 53 (2023), no. 6, 1691–1707.
  

• S. Atmani; A. Bayad;M-O. Hernane. Congruences for Fourier coefficients of eta-quotients modulo powers of 5, 7, 11, 13, and 17. Math. Methods Appl. Sci. 46 (2023), no. 5, 5001–5028.
  

• A. Bayad; M. Hajli. On Jacobi forms, and explicit evaluations of some trigonometric sums. Ramanujan J 60, 27–57 (2023).
  

• A. Bayad; G.J. Hwan; D.Kim. Convolution sum of Ramanujan's sum. Journal of Applied and Pure Mathematics, 2022, 4 (1-2), pp.63-69.
  

• A. Bayad; M. Hajli. The extended Eulerian numbers over function fields. Appl. Anal. Discrete Math. 16 (2022), no. 2, 508–523.
  

• M. Ayad; A. Bayad; O. Kihel. On fixed divisors of the values of the minimal polynomials over ℤ of algebraic numbers. Hardy-Ramanujan J. 45 (2022), 57–73.
  

• A. Bayad; Ch. Khattou; M-O. Hernane. New results on Bernoulli numbers of higher order. Rocky Mountain J. Math. 52 (2022), no. 1, 153–170.
  

• A. Bayad; M. Hajli. The extended Eulerian numbers over function fields. Appl. Anal. Discrete Math. 16 (2022), no. 2, 508–523.
  

• A. Bayad; D. Kim; S-H. Park. Iterated stable numbers and iterated amicable pairs. Math. Methods Appl. Sci. 44 (2021), no. 17, 12479–12499.
  

• A. Bayad;Y. Simsek. Multiple Dedekind Type Sums and Their Related Zeta Functions. Mathematics 2021, 9(15), 1744.
  

• A. Bayad; M. Seddik. On the indices in number fields and their computation for small degrees. Appl. Anal. Discrete Math. 15 (2021), no. 1, 27–44.
  

• A. Bayad; Y. Simsek. p-Adic q-Twisted Dedekind-Type Sums. Symmetry 2021, 13(9), 1756.
  

• A. Bayad; M. Seddik. Index, the prime ideal factorization in simplest quartic fields and counting their discriminants. Filomat 34 (2020), no. 2, 591–600.
  

• A. Bayad; D. Kim; H. Ahn. A study of Möbius-Bernoulli numbers. Appl. Anal. Discrete Math. 14 (2020), no. 3, 719–728.
  

• A. Bayad; M. Hajli. On the multidimensional zeta functions associated with theta functions, and the multidimensional Appell polynomials. Math. Methods Appl. Sci. 43 (2020), no. 5, 2679–2694.
  

• A. Bayad. Jacobi forms in two variables: multiple elliptic Dedekind sums, the Kummer-Von Staudt Clausen congruences for elliptic Bernoulli functions and values of Hecke L-functions, Montes Taurus J. Pure Appl. Math. 1 (2), 58–129, 2019.
  

• A. Bayad; M. Seddik. On cubic Thue equations and the indices of algebraic integers in cubic fields. Appl. Anal. Discrete Math. 13 (2019), no. 3, 774–786.
  

• . Ch. Adiga; A. Bayad; D. Ranganatha. Some new congruences for (s,t)-regular bipartition functions. Publ. Inst. Math. (Beograd) (N.S.) 106(120) (2019), 53–67.
  

• A. Bayad; D. Kim; Y. Li. Arithmetical properties of double Möbius-Bernoulli numbers. Open Math. 17 (2019), no. 1, 32–42.
  

• A. Bayad; M. Goubi. Reciprocity formulae for generalized Dedekind-Vasyunin-cotangent sums. Math. Methods Appl. Sci. 42 (2019), no. 4, 1082–1098.
  

• A. Bayad; T. Komatsu. Zeta functions interpolating the convolution of the Bernoulli polynomials. Integral Transforms Spec. Funct. 29 (2018), no. 8, 611–622.
  

• A. Bayad; D. Kim. Mean Values of Products of L-Functions and Bernoulli Polynomials. Mathematics (2018), 6(12), 337.
  

• J.S. Auli; A. Bayad; M. Beck. Reciprocity theorems for Bettin-Conrey sums. Acta Arith. 181 (2017), no. 4, 297–319.
  

• A. Bayad; M. Goubi;M-O. Hernane. Explicit and asymptotic formulae for Vasyunin-cotangent sums. Publ. Inst. Math. (Beograd) (N.S.) 102(116) (2017), 155–174.
  

• A. Bayad;I.Kucukoglu;Y. Simsek, k-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-Lerch zeta function and Apostol-Bernoulli polynomials. Mediterr. J. Math. 14 (2017), no. 6, Paper No. 223, 16 pp.
  

• A. Bayad; D. Kim. Polygon numbers associated with the sum of odd divisors function. Exp. Math. 26 (2017), no. 3, 287–297.
  

• A. Bayad; T. Komatsu. New characterization of Appell polynomials. Integral Transforms Spec. Funct. 28 (2017), no. 3, 212–222.
  

• A. Bayad; D.D. Somashekara; K. Narasimha Murthy, On finite forms of Bailey's 2ψ2 transformation formulae and their applications. Int. J. Number Theory 12 (2016), no. 8, 2189–2200.
  

• A. Bayad; M-O.Hernane; A. Togbé. On extended Eulerian numbers.Funct. Approx. Comment. Math. 55 (2016), no. 1, 113–130.
  

• A. Bayad; T. Kim. Identities for Apostol-type Frobenius-Euler polynomials resulting from the study of a nonlinear operator. Russ. J. Math. Phys. 23 (2016), no. 2, 164–171.
  

• A. Bayad; G. Robert. The Jacobi form D_L, theta functions, and Eisenstein series. J. Théor. Nombres Bordeaux 28 (2016), no. 1, 75–88.
  

• A. Bayad; L. Navas. Möbius inversion formulas related to the Fourier expansions of two-dimensional Apostol-Bernoulli polynomials. J. Number Theory 163 (2016), 457–473.
  

• A. Bayad; L. Navas. Algebraic properties and Fourier expansions of two-dimensional Apostol-Bernoulli and Apostol-Euler polynomials. Appl. Math. Comput. 265 (2015), 883–892.
  

• A. Bayad; D. Kim; Y. Nazli. Certain combinatoric convolution sums and their relations to Bernoulli and Euler polynomials. J. Korean Math. Soc. 52 (2015), no. 3, 537–565.
  

• M. Ayad; A. Bayad; O. Kihel. Denominators of algebraic numbers in a number field. J. Number Theory 149 (2015), 1–14.
  

• A. Bayad; Y. Hamahata. Multiple Dedekind-Rademacher sums in finite fields. Ramanujan J. 35 (2014), no. 3, 493–502.
  

• A. Bayad; D. Kim; J.Park. Euler polynomials and combinatoric convolution sums of divisor functions with even indices. Abstr. Appl. Anal.(2014), Art. ID 289187, 6 pp.
  

• A. Bayad; H.M. Srivastava; S. Gaboury. Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus. Adv. Difference Equ.(2014), 2014:169, 17 pp.
  

• A. Bayad; Y. Simsek, Yilmaz; H. M. Srivastava. Some array type polynomials associated with special numbers and polynomials. Appl. Math. Comput. 244 (2014), 149–157.
  

• A. Bayad; M. Beck. Relations for Bernoulli-Barnes numbers and Barnes zeta functions. Int. J. Number Theory 10 (2014), no. 5, 1321–1335.
  

• A. Bayad; Y. Hamahata. Multiple Dedekind-Rademacher sums in function fields. Int. J. Number Theory 10 (2014), no. 5, 1291–1307.
  

• A. Bayad; Y. Simsek. Convolution identities on the Apostol-Hermite base of two variables polynomials. Differ. Equ. Dyn. Syst. 22 (2014), no. 3, 309–318.
  

• A. Bayad; J. Chikhi. Apostol-Euler polynomials and asymptotics for negative binomial reciprocals. Adv. Stud. Contemp. Math. (Kyungshang) 24 (2014), no. 1, 33–37.
  

• A. Bayad; J. Chikhi. Möbius inversion formulae for apostol-bernoulli type polynomials and numbers. Mathematics of Computation, 2013, 82(284), pp. 2327–2332
  

• A. Bayad; S. Gaboury. Generalized dirichlet L-function of arbitrary order with applications. Advanced Studies in Contemporary Mathematics (Kyungshang), 2013, 23(4), pp. 607–619.
  

• A. Bayad; T.Kim. Results on values of Barnes polynomials. Rocky Mountain J. Math. 43 (2013), no. 6, 1857–1869.
  

• A. Bayad; S. Gaboury. Series representations at special values of generalized Hurwitz-Lerch zeta function. Abstr. Appl. Anal.(2013), Art. ID 975615, 8 pp.
  

• A. Bayad; M. Goubi. Proof of the Möbius conjecture revisited. Proc. Jangjeon Math. Soc. 16 (2013), no. 2, 237–243.
  

• A. Bayad; A.R. Bindusree; V. Lokesha; P.S. Ranjini. Relation connecting Zagreb co-indices on three graph operators. Math. Æterna 3 (2013), no. 5-6, 433–448.
  

• A. Bayad; T.Kim,W.J. Kim, S.H. Lee. Arithmetic properties of q-Barnes polynomials. Journal of Computational Analysis and Applications, 2013, 15(1), pp. 111–117.
  

• A. Bayad; Y. Simsek; V. Lokesha. q-Bernstein polynomials related to q-Frobenius-Euler polynomials, l-functions, and q-Stirling numbers. Math. Methods Appl. Sci. 35 (2012), no. 8, 877–884.
  

• A. Bayad; A. Raouj. Mean values of L-functions and Dedekind sums. J. Number Theory 132 (2012), no. 8, 1645–1652.
  

• A. Bayad; Y. Hamahata. Identities involving two kinds of q-Euler polynomials and numbers. J. Integer Seq. 15 (2012), no. 4, Article 12.4.6, 14 pp.
  

• A. Bayad; T. Kim. Higher recurrences for Apostol-Bernoulli-Euler numbers. Russ. J. Math. Phys. 19 (2012), no. 1, 1–10.
  

• A. Bayad; I. N. Cangul. The minimal polynomial of 2cos(π/q) and Dickson polynomials. Appl. Math. Comput. 218 (2012), no. 13, 7014–7022.
  

• A. Bayad; Y. Hamahata. Higher dimensional Dedekind sums in finite fields. Finite Fields Appl. 18 (2012), no. 1, 19–25.
  

• A. Bayad; Y. Hamahata. Higher dimensional Dedekind sums in function fields. Acta Arith. 152 (2012), no. 1, 71–80.
  

• A. Bayad; A. Raouj. Arithmetic of higher dimensional Dedekind-Rademacher sums. J. Number Theory 132 (2012), no. 2, 332–347.
  

• A. Bayad. Special values of Lerch zeta function and their Fourier expansions. Adv. Stud. Contemp. Math. (Kyungshang) 21 (2011), no. 1, 1–4.
  

• A. Bayad; Y. Simsek. Dedekind sums involving Jacobi modular forms and special values of Barnes zeta functions. Ann. Inst. Fourier (Grenoble) 61 (2011), no. 5, 1977–1993.
  

• A. Bayad; T. Kim; S.H. Lee; D.V. Dolgy. A note on the generalized Bernstein polynomials. Honam Math. J. 33 (2011), no. 3, 431–439.
  

• A. Bayad; S-H. Rim; E-J. Moon; S-J. Lee. |A new construction on the q-Bernoulli polynomials. Adv. Difference Equ.(2011), 2011:34, 6 pp.
  

• A. Bayad. Fourier expansions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. Math. Comp. 80 (2011), no. 276, 2219–2221.
  

• A. Bayad; T. Kim. Identities involving values of Bernstein, q-Bernoulli, and q-Euler polynomials. Russ. J. Math. Phys. 18 (2011), no. 2, 133–143.
  

• A. Bayad; Y.Hamahata. Polylogarithms and poly-Bernoulli polynomials. Kyushu J. Math. 65 (2011), no. 1, 15–24.
  

• A. Bayad; T. Kim; J.Choi; Y.H.Kim;B. Lee.On the symmetry properties of the generalized higher-order Euler polynomials. J. Appl. Math. Inform. 29 (2011), no. 1-2, 511–516.
  

• A. Bayad; T. Kim; B. Lee; S-H. Rim.Some identities on Bernstein polynomials associated with q-Euler polynomials. Abstr. Appl. Anal.(2011), Art. ID 294715, 10 pp.
  

• A. Bayad; Y. Hamahata. Arakawa-Kaneko L-functions and generalized poly-Bernoulli polynomials. J. Number Theory 131 (2011), no. 6, 1020–1036.
  

• A. Bayad; A. Raouj. Reciprocity formulae for multiple Dedekind-Rademacher sums. C. R. Math. Acad. Sci. Paris 349 (2011), no. 3-4, 131–136.
  

• A. Bayad; T. Kim; Y.H. Kim. A study on the p-adic q-integral representation on ℤp associated with the weighted q-Bernstein and q-Bernoulli polynomials. J. Inequal. Appl.(2011), Art. ID 513821, 8 pp.
  

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• A. Bayad; A. Raouj. Reciprocity formulae for general multiple Dedekind-Rademacher sums and enumeration of lattice points. Acta Arith. 145 (2010), no. 2, 137–154.
  

• A. Bayad. Modular properties of elliptic Bernoulli and Euler functions. Adv. Stud. Contemp. Math. (Kyungshang) 20 (2010), no. 3, 389–401.
  

• A. Bayad; V. Lokesha; B.N. Kumar; K.M. Nagraja; M. Saraj. New means and its properties. Proc. Jangjeon Math. Soc. 13 (2010), no. 2, 243–254.
  

• A. Bayad; T.Kim. Identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials. Adv. Stud. Contemp. Math. (Kyungshang) 20 (2010), no. 2, 247–253.
  

• A. Bayad; A. Ganesh; G. Balasubramanian. On the |N⎯⎯⎯⎯,pn|k summability of factored Fourier series. Int. Math. Forum 5 (2010), no. 21-24, 1067–1073.
  

• A. Bayad. Arithmetical properties of elliptic Bernoulli and Euler numbers. Int. J. Algebra 4 (2010), no. 5-8, 353–372.
  

• A. Bayad. On values of Jacobi forms and elliptic Dedekind sums.Proc. Jangjeon Math. Soc. 12 (2009), no. 2, 119–139.
  

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• A. Bayad. Applications aux sommes elliptiques d'Apostol-Dedekind-Zagier Applications to elliptic Apostol-Dedekind-Zagier sums. C. R. Math. Acad. Sci. Paris 339 (2004), no. 8, 529–532.
  

• A. Bayad. Sommes elliptiques multiples d'Apostol-Dedekind-Zagier Multiple elliptic Apostol-Dedekind-Zagier sums. C. R. Math. Acad. Sci. Paris 339 (2004), no. 7, 457–462.
  

• A. Bayad; J. Gomez Ayala. Formes de Jacobi et formules de distribution Jacobi forms and distribution formulas. J. Number Theory 109 (2004), no. 1, 136–162.
  

• A. Bayad. Sommes de Dedekind elliptiques et formes de Jacobi Elliptic Dedekind sums and Jacobi forms. Ann. Inst. Fourier (Grenoble) 51 (2001), no. 1, 29–42.
  

• A. Bayad. Formes de Jacobi et formule de Weber p-adiqueJacobi forms and p-adic Weber formula. J. Théor. Nombres Bordeaux 11 (1999), no. 2, 317–329.
  
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• A. Bayad; G. Robert. Note on a meromorphic Jacobi form. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 5, 455–460.
  

• A. Bayad; G. Robert. Amélioration d'une congruence pour certains éléments de Stickelberger quadratiques. Improvement of a congruence for certain quadratic Stickelberger elements. Bull. Soc. Math. France 125 (1997), no. 2, 249–267.
  

• A. Bayad. Valuation q-adique et relation de distribution additive pour certaines fonctions q-périodiques q-adic valuation and additive distribution relation for certain q-periodic functions. J. Number Theory 65 (1997), no. 1, 1–22.
  

• A. Bayad; W. Bley; Ph. Cassou-Noguès.Sommes arithmétiques et éléments de Stickelberger Arithmetical sums and Stickelberger elements. J. Algebra 179 (1996), no. 1, 145–190.
  

• A. Bayad. Loi de réciprocité quadratique dans les corps quadratiques imaginaires. Quadratic reciprocity law in imaginary quadratic fields. Ann. Inst. Fourier (Grenoble) 45 (1995), no. 5, 1223–1237.
  

• A. Bayad. Structure galoisienne d'anneaux d'entiers et courbes elliptiques sans multiplication complexe Galois structure of rings of integers and elliptic curves without complex multiplication. J. Number Theory 52 (1995), no. 2, 267–279.
  

• Abdelmejid Bayad; Mustafa Alkan; Irem Kucukoglu , Ortaç Önes. PROCEEDINGS BOOK of MICOPAM 2023 The 6thMediterranean International Conference of Pure & Applied Mathematics and Related Areas(MICOPAM 2023), 2024, 978-2-491766-0-6 .
  

• Abdelmejid Bayad; Y. Simsek. Recent Advances in Number Theory and Their Applications. Symmetry (ISSN 2073-8994), (2021).
  

• Abdelmejid Bayad; Mustafa Alkan ; Irem Kucukoglu ; Ortaç Önes, Yilmaz Simsek. PROCEEDINGS BOOK of the 2th Mediterranean International Conference of Pure & Applied Mathematics and Related Areas (MICOPAM 2019), 2020, 978-2-491766-00-9.
  

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• Responsable de la Licence 1 Mathématiques de 2016 à 2019
  
• Responsable du portail Mathématiques et Informatique: 2020 --- .
  

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