Mihran Papikian

    • 60 Citations
    • 4 h-Index
    20012019
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    Research Output 2001 2019

    • 60 Citations
    • 4 h-Index
    • 28 Article
    2019

    Endomorphism rings of reductions of Drinfeld modules

    Garai, S. & Papikian, M., Jan 1 2019, In : Journal of Number Theory.

    Research output: Contribution to journalArticle

    Drinfeld Modules
    Endomorphism Ring
    Divides
    Reciprocity Law
    Integral Closure
    2018

    On Ribet’s isogeny for J0 (65)

    Klosin, K. & Papikian, M., Jan 1 2018, In : Proceedings of the American Mathematical Society. 146, 8, p. 3307-3320 14 p.

    Research output: Contribution to journalArticle

    Isogeny
    Algebra
    Isogenies
    kernel
    Quaternion Algebra
    2017
    1 Citation (Scopus)

    The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains

    Papikian, M. & Wei, F. T., Dec 26 2017, In : Mathematische Zeitschrift. 287, 1-2, p. 521-546 26 p.

    Research output: Contribution to journalArticle

    Divisor Class Group
    Torsion
    Harmonic
    Subgroup
    Jacobian Varieties
    2016

    On component groups of Jacobians of quaternionic modular curves

    Papikian, M., Oct 1 2016, In : Archiv der Mathematik. 107, 4, p. 315-328 14 p.

    Research output: Contribution to journalArticle

    Modular Curves
    Quaternion Algebra
    Finite Graph
    Weighted Graph
    Discriminant

    On Garland’s vanishing theorem for SL n

    Papikian, M., Sep 1 2016, In : European Journal of Mathematics. 2, 3, p. 579-613 35 p.

    Research output: Contribution to journalArticle

    Vanishing Theorems
    Cohomology of Groups
    Linear Algebraic Groups
    Simplicial Complex
    Group Theory

    Optimal quotients of Jacobians with toric reduction and component groups

    Papikian, M. & Rabinoff, J., Dec 2016, In : Canadian Journal of Mathematics. 68, 6, p. 1362-1381 20 p.

    Research output: Contribution to journalArticle

    Quotient
    Jacobian Varieties
    Modular Curves
    Local Field
    Elliptic Curves
    2015
    2 Citations (Scopus)

    Drinfeld Modules, Frobenius Endomorphisms, and CM-Liftings

    Cojocaru, A. C. & Papikian, M., Jan 1 2015, In : International Mathematics Research Notices. 2015, 17, p. 7787-7825 39 p.

    Research output: Contribution to journalArticle

    Drinfeld Modules
    Endomorphisms
    Frobenius
    Endomorphism Ring
    Modulo
    4 Citations (Scopus)

    The eisenstein ideal and jacquet-langlands isogeny over function fields

    Papikian, M. & Wei, F. T., Jan 1 2015, In : Documenta Mathematica. 20, 2015, p. 551-630 80 p.

    Research output: Contribution to journalArticle

    Isogeny
    Function Fields
    Subgroup
    Isogenies
    Modular Curves
    2014
    1 Citation (Scopus)

    On the Eisenstein ideal over function fields

    Papikian, M. & Wei, F. T., Oct 7 2014, In : Journal of Number Theory. 161, p. 384-434 51 p.

    Research output: Contribution to journalArticle

    Function Fields
    Modular Curves
    Prime number
    Divisor
    Arbitrary
    2013

    D-elliptic sheaves and odd Jacobians

    Papikian, M., Mar 1 2013, In : Journal of Number Theory. 133, 3, p. 1012-1026 15 p.

    Research output: Contribution to journalArticle

    Sheaves
    Quotient
    Odd
    Modular Curves
    Local Field
    2012
    8 Citations (Scopus)

    Local diophantine properties of modular curves of D-elliptic sheaves

    Papikian, M., Jan 1 2012, In : Journal fur die Reine und Angewandte Mathematik. 2012, 664, p. 115-140 26 p.

    Research output: Contribution to journalArticle

    Modular Curves
    Sheaves
    Algebra
    Hasse Principle
    Arithmetic Groups
    2011
    2 Citations (Scopus)

    On finite arithmetic simplicial complexes

    Papikian, M., Jan 1 2011, In : Proceedings of the American Mathematical Society. 139, 1, p. 111-124 14 p.

    Research output: Contribution to journalArticle

    Rational functions
    Simplicial Complex
    Algebra
    Quotient
    Bruhat-Tits Building

    On generators of arithmetic groups over function fields

    Papikian, M., Sep 1 2011, In : International Journal of Number Theory. 7, 6, p. 1573-1587 15 p.

    Research output: Contribution to journalArticle

    Arithmetic Groups
    Quaternion Algebra
    Group of Units
    Division Algebra
    Subring
    6 Citations (Scopus)

    On Jacquet-Langlands isogeny over function fields

    Papikian, M., Jul 1 2011, In : Journal of Number Theory. 131, 7, p. 1149-1175 27 p.

    Research output: Contribution to journalArticle

    Isogeny
    Function Fields
    Modular Curves
    Divisor
    Hyperelliptic Curves
    2010
    3 Citations (Scopus)

    Endomorphisms of exceptional D-elliptic sheaves

    Papikian, M., Jan 1 2010, In : Mathematische Zeitschrift. 266, 2, p. 407-423 17 p.

    Research output: Contribution to journalArticle

    Endomorphism Ring
    Division Algebra
    Endomorphisms
    Function Fields
    Sheaves
    2009
    5 Citations (Scopus)

    Genus formula for modular curves of D -elliptic sheaves

    Papikian, M., Mar 1 2009, In : Archiv der Mathematik. 92, 3, p. 237-250 14 p.

    Research output: Contribution to journalArticle

    Modular Curves
    Sheaves
    Genus
    Discriminant
    Infinity
    1 Citation (Scopus)

    Modular varieties of D-elliptic sheaves and the Weil-Deligne bound

    Papikian, M., Jan 1 2009, In : Journal fur die Reine und Angewandte Mathematik. 626, p. 115-134 20 p.

    Research output: Contribution to journalArticle

    Sheaves
    Modular Curves
    Betti numbers
    Rational Points
    Asymptotically Optimal
    3 Citations (Scopus)

    On hyperelliptic modular curves over function fields

    Papikian, M., Apr 1 2009, In : Archiv der Mathematik. 92, 4, p. 291-302 12 p.

    Research output: Contribution to journalArticle

    Modular Curves
    Hyperelliptic Curves
    Function Fields
    Sheaves
    Odd
    2008

    Modular curves of D-elliptic sheaves are asymptotically optimal

    Papikian, M., Mar 1 2008, In : Mathematical Research Letters. 15, 2-3, p. 525-536 12 p.

    Research output: Contribution to journalArticle

    Modular Curves
    Asymptotically Optimal
    Sheaves
    Series
    2 Citations (Scopus)

    On eigenvalues of p-adic curvature

    Papikian, M., Nov 1 2008, In : Manuscripta Mathematica. 127, 3, p. 397-410 14 p.

    Research output: Contribution to journalArticle

    P-adic
    Curvature
    Eigenvalue
    Buildings
    2007
    2 Citations (Scopus)

    Abelian subvarieties of Drinfeld Jacobians and congruences modulo the characteristic

    Papikian, M., Jan 1 2007, In : Mathematische Annalen. 337, 1, p. 139-157 19 p.

    Research output: Contribution to journalArticle

    Congruence
    Modulo
    Modular Curves
    Cusp Form
    Frobenius
    4 Citations (Scopus)

    Analogue of the degree conjecture over function fields

    Papikian, M., Jul 1 2007, In : Transactions of the American Mathematical Society. 359, 7, p. 3483-3503 21 p.

    Research output: Contribution to journalArticle

    Modular Curves
    Function Fields
    Parametrization
    Elliptic Curves
    Upper bound
    2006
    3 Citations (Scopus)

    On the torsion of optimal elliptic curves over function fields

    Papikian, M., Jan 1 2006, In : Mathematical Research Letters. 13, 2-3, p. 321-331 11 p.

    Research output: Contribution to journalArticle

    Function Fields
    Conductor
    Elliptic Curves
    Divisor
    Torsion
    Modular Curves
    Rational Points
    Galois field
    Genus
    High-dimensional
    2005
    4 Citations (Scopus)

    On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves

    Papikian, M., Dec 1 2005, In : Journal of Number Theory. 115, 2, p. 249-283 35 p.

    Research output: Contribution to journalArticle

    Hyperelliptic Curves
    Elliptic Curves
    Irreducible polynomial
    Prime Ideal
    Conductor
    4 Citations (Scopus)

    Pesenti-Szpiro inequality for optimal elliptic curves

    Papikian, M., Oct 1 2005, In : Journal of Number Theory. 114, 2, p. 361-393 33 p.

    Research output: Contribution to journalArticle

    Conductor
    Discriminant
    Elliptic Curves
    Jacobian Varieties
    Modular Curves
    2002
    5 Citations (Scopus)

    On the degree of modular parametrizations over function fields

    Papikian, M., Dec 1 2002, In : Journal of Number Theory. 97, 2, p. 317-349 33 p.

    Research output: Contribution to journalArticle

    Function Fields
    Parametrization
    Modular Curves
    Conductor
    Elliptic Curves
    2001

    On coset coverings of solutions of homogeneous cubic equations over finite fields

    Aleksanyan, A. & Papikian, M., Dec 1 2001, In : Electronic Journal of Combinatorics. 8, 1 R, p. 1-9 9 p.

    Research output: Contribution to journalArticle

    Cubic equation
    Coset
    Linear equations
    Galois field
    Covering