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  1. Research

    A problem of Petersson about weight 0 meromorphic modular forms

    In this paper, we provide an explicit construction of weight 0 meromorphic modular forms. Following work of Petersson, we build these via Poincaré series. There are two main aspects of our investigation which ...

    Kathrin Bringmann and Ben Kane

    Research in the Mathematical Sciences 2016 3:24

    Published on: 1 December 2016

  2. Research

    Vanishing theorems for coherent automorphic cohomology

    We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties (such as Shimura varieties) with coefficients in the canonical and subcanonical extensions of automorphic vector...

    Kai-Wen Lan

    Research in the Mathematical Sciences 2016 3:39

    Published on: 10 November 2016

  3. Research

    The Morse–Bott–Kirwan condition is local

    Kirwan identified a condition on a smooth function under which the usual techniques of Morse–Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it al...

    Tara Holm and Yael Karshon

    Research in the Mathematical Sciences 2016 3:25

    Published on: 7 November 2016

  4. Research

    Average values of L-series for real characters in function fields

    We establish asymptotic formulae for the first and second moments of quadratic Dirichlet L-functions, at the center of the critical strip, associated to the real quadratic function field ...

    Julio C. Andrade, Sunghan Bae and Hwanyup Jung

    Research in the Mathematical Sciences 2016 3:38

    Published on: 2 November 2016

  5. Research

    Some properties of dynamical degrees with a view towards cubic fourfolds

    Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degre...

    Christian Böhning, Hans-Christian Graf von Bothmer and Pawel Sosna

    Research in the Mathematical Sciences 2016 3:23

    Published on: 1 November 2016

  6. Research

    On the rigid cohomology of certain Shimura varieties

    We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of

    Michael Harris, Kai-Wen Lan, Richard Taylor and Jack Thorne

    Research in the Mathematical Sciences 2016 3:37

    Published on: 26 October 2016

  7. Research

    Rankin–Eisenstein classes in Coleman families

    We show that the Euler system associated with Rankin–Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in p-adic Coleman fami...

    David Loeffler and Sarah Livia Zerbes

    Research in the Mathematical Sciences 2016 3:29

    Published on: 1 October 2016

  8. Research

    The adic, cuspidal, Hilbert eigenvarieties

    We construct adic, compactified eigenvarieties parameterizing adic overconvergent Hilbert modular eigenforms of finite slope by constructing integral families of modular sheaves on the relevant formal Shimura ...

    Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni

    Research in the Mathematical Sciences 2016 3:34

    Published on: 8 September 2016

  9. Research

    Elliptic curves of rank two and generalised Kato classes

    Heegner points play an outstanding role in the study of the Birch and Swinnerton-Dyer conjecture, providing canonical Mordell–Weil generators whose heights encode first derivatives of the associated Hasse–Weil L-...

    Henri Darmon and Victor Rotger

    Research in the Mathematical Sciences 2016 3:27

    Published on: 24 August 2016

  10. Research

    On the regulator formulas of Bertolini, Darmon and Rotger

    We give a unified, and somewhat simplified, account of the regulator formulas appearing in papers of Bertolini, Darmon and Rotger, describing the syntomic regulator on the first, second and third self-products...

    Amnon Besser

    Research in the Mathematical Sciences 2016 3:26

    Published on: 22 August 2016


    Geometric and analytic structures on the higher adèles

    The adèles of a scheme have local components—these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies ...

    O. Braunling, M. Groechenig and J. Wolfson

    Research in the Mathematical Sciences 2016 3:22

    Published on: 15 August 2016

  12. Research

    Exact triangle for fibered Dehn twists

    We use quilted Floer theory to generalize Seidel’s long exact sequence in symplectic Floer theory to fibered Dehn twists. We then apply the sequence to construct versions of the Floer and Khovanov–Rozansky exa...

    Katrin Wehrheim and Chris T. Woodward

    Research in the Mathematical Sciences 2016 3:17

    Published on: 15 August 2016

  13. Research

    Higgs bundles and exceptional isogenies

    We explore relations between Higgs bundles that result from isogenies between low-dimensional Lie groups, with special attention to the spectral data for the Higgs bundles. We focus on isogenies onto

    Steven B. Bradlow and Laura P. Schaposnik

    Research in the Mathematical Sciences 2016 3:14

    Published on: 1 August 2016

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