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  1. Content type: Research

    Given a family X of complex varieties degenerating over a punctured disk, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which...

    Authors: Alan Stapledon

    Citation: Research in the Mathematical Sciences 2017 4:8

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  2. Content type: Research

    We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, str...

    Authors: Ludvig af Klinteberg, Davoud Saffar Shamshirgar and Anna-Karin Tornberg

    Citation: Research in the Mathematical Sciences 2017 4:1

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  3. Content type: Research

    We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentu...

    Authors: Wenjia Jing, Panagiotis E. Souganidis and Hung V. Tran

    Citation: Research in the Mathematical Sciences 2017 4:6

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  4. Content type: Research

    In this paper, we prove the existence of an infinite-dimensional graded supermodule for the finite sporadic Thompson group Th whose McKay–Thompson series are weakly holomorphic modular forms of weight

    Authors: Michael J. Griffin and Michael H. Mertens

    Citation: Research in the Mathematical Sciences 2016 3:36

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  5. Content type: Research

    This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators http://static-content.springer.com/image/art%3A10.1186%2Fs40687-016-0082-9/40687_2016_82_Article_IEq1.gif

    Authors: Jeffrey C. Lagarias and Wen-Ching Winnie Li

    Citation: Research in the Mathematical Sciences 2016 3:33

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  6. Content type: Research

    We investigate Poincaré series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier ser...

    Authors: Kathrin Bringmann, Olav K. Richter and Martin Westerholt-Raum

    Citation: Research in the Mathematical Sciences 2016 3:30

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  7. Content type: Research

    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 ...

    Authors: Kathrin Bringmann and Ben Kane

    Citation: Research in the Mathematical Sciences 2016 3:24

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  8. Content type: Research

    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...

    Authors: Kai-Wen Lan

    Citation: Research in the Mathematical Sciences 2016 3:39

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  9. Content type: Research

    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...

    Authors: Tara Holm and Yael Karshon

    Citation: Research in the Mathematical Sciences 2016 3:25

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  10. Content type: Research

    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...

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

    Citation: Research in the Mathematical Sciences 2016 3:23

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  11. Content type: Research

    We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of http://static-content.springer.com/image/art%3A10.1186%2Fs40687-016-0078-5/40687_2016_78_Article_IEq1.gif

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

    Citation: Research in the Mathematical Sciences 2016 3:37

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  12. Content type: Research

    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...

    Authors: David Loeffler and Sarah Livia Zerbes

    Citation: Research in the Mathematical Sciences 2016 3:29

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