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  • 1. Bamunoba, Alex Samuel
    et al.
    Bergström, Jonas
    Stockholm University, Faculty of Science, Department of Mathematics.
    A search for c-Wieferich primes2021In: International Journal of Number Theory, ISSN 1793-0421, Vol. 17, no 07, p. 1599-1616Article in journal (Refereed)
    Abstract [en]

    Let q be a power of a prime number p, F-q be a finite field with q elements and G be a subgroup of (F-q,+) of order p. We give an existence criterion and an algorithm for computing maximally G-fixed c-Wieferich primes in F-q[T]. Using the criterion, we study how c-Wieferich primes behave in F-q[T] extensions.

  • 2.
    Berglund, Alexander
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bergström, Jonas
    Stockholm University, Faculty of Science, Department of Mathematics.
    Hirzebruch L-polynomials and multiple zeta values2018In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 372, no 1-2, p. 125-137Article in journal (Refereed)
    Abstract [en]

    We express the coefficients of the Hirzebruch L-polynomials in terms of certain alternating multiple zeta values. In particular, we show that every monomial in the Pontryagin classes appears with a non-zero coefficient, with the expected sign. Similar results hold for the polynomials associated to the Â-genus.

  • 3.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bergvall, Olof
    The equivariant Euler characteristic of A3[2]2020In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. XX, no 4, p. 1345-1357Article in journal (Refereed)
    Abstract [en]

    We compute the weighted Euler characteristic, equivariant with respect to the action of the symplectic group of degree six over the field of two elements, of the moduli space of principally polarized Abelian threefolds together with a level two structure. 

  • 4.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Dummigan, Neil
    Eisenstein congruences for split reductive groups2016In: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 22, no 3, p. 1073-1115Article in journal (Refereed)
    Abstract [en]

    We present a general conjecture on congruences between Hecke eigenvalues of parabolically induced and cuspidal automorphic representations of split reductive groups, modulo divisors of critical values of certain L-functions. We examine the consequences in several special cases and use the Bloch–Kato conjecture to further motivate a belief in the congruences.

  • 5.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Dummigan, Neil
    Farmer, David
    Koutsoliotas, Sally
    GL2 x GSp2 L-values and Hecke eigenvalue congruences2019In: Journal de Théorie des Nombres de Bordeaux, ISSN 1246-7405, E-ISSN 2118-8572, Vol. 31, no 3, p. 751-775Article in journal (Refereed)
    Abstract [en]

    We find experimental examples of congruences of Hecke eigenvalues between automorphic representations of groups such as GSp2(A), SO(4,3)(A) and SO(5,4)(A), where the prime modulus should, for various reasons, appear in the algebraic part of a critical “tensor-product” L-value associated to cuspidal automorphic representations of GL2(A) and GSp2(A). Using special techniques for evaluating L-functions with few known coefficients, we compute sufficiently good approximations to detect the anticipated prime divisors.

  • 6.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Dummigan, Neil
    Mégarbané, Thomas
    Ibukiyama, Tomoyoshi
    Katsurada, Hidenori
    Eisenstein Congruences for SO(4, 3), SO(4, 4), Spinor, and Triple Product L-values2018In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 27, no 2, p. 230-250Article in journal (Refereed)
    Abstract [en]

    We work out instances of a general conjecture on congruences between Hecke eigenvalues of induced and cuspidal automorphic representations of a reductive group, modulo divisors of certain critical L-values, in the case that the group is a split orthogonal group. We provide some numerical evidence in the case that the group is SO(4, 3) and the L-function is the spinor L-function of a genus 2, vector-valued, Siegel cusp form. We also consider the case that the group is SO(4, 4) and the L-function is a triple product L-function.

  • 7.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Faber, Carel
    van der Geer, Gerard
    Siegel modular forms of degree three and the cohomology of local systems2014In: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 20, no 1, p. 83-124Article in journal (Refereed)
    Abstract [en]

    We give an explicit conjectural formula for the motivic Euler characteristic of an arbitrary symplectic local system on the moduli space of principally polarized abelian threefolds. The main term of the formula is a conjectural motive of Siegel modular forms of a certain type; the remaining terms admit a surprisingly simple description in terms of the motivic Euler characteristics for lower genera. The conjecture is based on extensive counts of curves of genus three and abelian threefolds over finite fields. It provides a lot of new information about vector-valued Siegel modular forms of degree three, such as dimension formulas and traces of Hecke operators. We also use it to predict several lifts from genus 1 to genus 3, as well as lifts from and new congruences of Harder type.

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  • 8.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Minabe, Satoshi
    On the cohomology of moduli spaces of (weighted) stable rational curves2013In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 275, no 3-4, p. 1095-1108Article in journal (Refereed)
    Abstract [en]

    We give a recursive algorithm for computing the character of the cohomology of the moduli space of stable -pointed genus zero curves as a representation of the symmetric group on letters. Using the algorithm we can show a formula for the maximum length of this character. Our main tool is connected to the moduli spaces of weighted stable curves introduced by Hassett.

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    fulltext
  • 9.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Minabe, Satoshi
    On the cohomology of the Losev–Manin moduli space2014In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 144, no 1, p. 241-252Article in journal (Refereed)
    Abstract [en]

    We determine the cohomology of the Losev--Manin moduli space $\overline{M}_{0, 2 | n}$ of pointed genus zero curves as a representation of the product of symmetric groups $\Sg_2 \times \Sg_n$.

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    fulltext
  • 10.
    Bergström, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Van der Geer, Gerard
    Picard modular forms and the cohomology of local systems on a Picard modular surface2022In: Commentarii Mathematici Helvetici, ISSN 0010-2571, E-ISSN 1420-8946, Vol. 97, no 2, p. 305-381Article in journal (Refereed)
    Abstract [en]

    We formulate a detailed conjectural Eichler–Shimura type formula for the cohomology of local systems on a Picard modular surface associated to the group of unitary similitudes GU(2, 1,  Q (√-3)). The formula is based on counting points over finite fields on curves of genus three which are cyclic triple covers of the projective line. Assuming the conjecture we are able to calculate traces of Hecke operators on spaces of Picard modular forms. We provide ample evidence for the conjectural formula.

    Along the way we prove new results on characteristic polynomials of Frobenius acting on the first cohomology group of cyclic triple covers of any genus, dimension formulas for spaces of Picard modular forms and formulas for the numerical Euler characteristics of the local systems.

  • 11. Ferrari, Eugenia
    et al.
    Tirabassi, Sofia
    Stockholm University, Faculty of Science, Department of Mathematics.
    Vodrup, Magnus
    Bergström, Jonas
    Stockholm University, Faculty of Science, Department of Mathematics.
    On the Brauer group of bielliptic surfaces (with an appendix by Jonas Bergström and Sofia Tirabassi)2022In: Documenta Mathematica, ISSN 1431-0635, E-ISSN 1431-0643, Vol. 27, p. 383-425Article in journal (Refereed)
    Abstract [en]

    We provide explicit generators of the torsion of the second cohomology of bielliptic surfaces, and we use this to study the pullback map between the Brauer group of a bielliptic surface and that of its canonical cover.

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