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  1. Content type: Review

    Monstrous moonshine relates distinguished modular functions to the representation theory of the Monster http://static-content.springer.com/image/art%3A10.1186%2Fs40687-015-0029-6/MediaObjects/40687_2015_29_Figa_HTML.gif . The celebrated observations that

    Authors: John FR Duncan, Michael J Griffin and Ken Ono

    Citation: Research in the Mathematical Sciences 2015 2:11

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  2. Content type: Research

    Let K be an algebraically closed, complete non-Archimedean field. The purpose of this paper is to carefully study the extent to which finite morphisms of algebraic K-curves are controlled by certain combinatorial...

    Authors: Omid Amini, Matthew Baker, Erwan Brugallé and Joseph Rabinoff

    Citation: Research in the Mathematical Sciences 2015 2:7

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  3. Content type: Research

    In this paper, we study the distribution of orders of bounded discriminants in number fields. We use the zeta functions introduced by Grunewald, Segal, and Smith. In order to carry out our study, we use p-adic...

    Authors: Nathan Kaplan, Jake Marcinek and Ramin Takloo-Bighash

    Citation: Research in the Mathematical Sciences 2015 2:6

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  4. Content type: Research

    We study the moduli space of metric graphs that arise from tropical plane curves. There are far fewer such graphs than tropicalizations of classical plane curves. For fixed genus g, our moduli space is a stacky f...

    Authors: Sarah Brodsky, Michael Joswig, Ralph Morrison and Bernd Sturmfels

    Citation: Research in the Mathematical Sciences 2015 2:4

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  5. Content type: Research

    We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalise the correspondence of facets of a polytope with the vertices of the dual polytope to g...

    Authors: Rainer Sinn

    Citation: Research in the Mathematical Sciences 2015 2:3

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  6. Content type: Research

    In this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2,2t+1). We use this to define a family of q-series, the simples...

    Authors: Kazuhiro Hikami and Jeremy Lovejoy

    Citation: Research in the Mathematical Sciences 2015 2:2

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  7. Content type: Research Article

    Nahm sums are q-series of a special hypergeometric type that appear in character formulas in the conformal field theory, and give rise to elements of the Bloch group, and have interesting modularity properties. I...

    Authors: Stavros Garoufalidis and Thang TQ Lê

    Citation: Research in the Mathematical Sciences 2015 2:1

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  8. Content type: Research Article

    Recently, a beautiful paper of Andrews and Sellers has established linear congruences for the Fishburn numbers modulo an infinite set of primes. Since then, a number of authors have proven refined results, for...

    Authors: Pavel Guerzhoy, Zachary A Kent and Larry Rolen

    Citation: Research in the Mathematical Sciences 2014 1:17

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  9. Content type: Research

    Cryo-electron microscopy is a technique in structural biology for determining the 3D structure of macromolecules. A key step in this process is detecting common lines of intersection between unknown embedded i...

    Authors: David Dynerman

    Citation: Research in the Mathematical Sciences 2014 1:14

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  10. Content type: Research

    In this paper, we consider the Fourier coefficients of a special class of meromorphic Jacobi forms of negative index considered by Kac and Wakimoto. Much recent work has been done on such coefficients in the c...

    Authors: Kathrin Bringmann, Thomas Creutzig and Larry Rolen

    Citation: Research in the Mathematical Sciences 2014 1:11

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  11. Content type: Research

    We give a new interpretation of Koszul cohomology, which is equivalent under the Bridgeland-King-Reid equivalence to Voisin’s Hilbert scheme interpretation in dimensions 1 and 2 but is different in higher dime...

    Authors: David H Yang

    Citation: Research in the Mathematical Sciences 2014 1:10

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  12. Content type: Research

    Don Zagier suggested a natural construction, which associates a real number and p-adic numbers for all primes p to the cusp form g=Δ of weight 12. He claimed that these quantities constitute a rational adele. In ...

    Authors: Pavel Guerzhoy

    Citation: Research in the Mathematical Sciences 2014 1:7

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  13. Content type: Research

    Almost 40 years ago, H. Cohen formulated a conjecture about the modularity of a certain infinite family of functions involving the generating function of the Hurwitz class numbers of binary quadratic forms.

    Authors: Michael H Mertens

    Citation: Research in the Mathematical Sciences 2014 1:6

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  14. Content type: Research

    A new and exciting breakthrough due to Maynard establishes that there exist infinitely many pairs of distinct primes p1, p2 with |p1-p2| ≤ 600 as a consequence of the Bombieri-Vinogradov Theorem. In this paper, w...

    Authors: Jesse Thorner

    Citation: Research in the Mathematical Sciences 2014 1:4

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  15. Content type: Research

    In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field, we found that the moments (mean, variance, and higher moments) of novel statistics on set p...

    Authors: Bobbie Chern, Persi Diaconis, Daniel M Kane and Robert C Rhoades

    Citation: Research in the Mathematical Sciences 2014 1:2

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  16. Content type: Research

    In this paper, we relate umbral moonshine to the Niemeier lattices - the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice, we attach a finite gro...

    Authors: Miranda CN Cheng, John FR Duncan and Jeffrey A Harvey

    Citation: Research in the Mathematical Sciences 2014 1:3

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