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High-Impact Research from The Quarterly Journal of Mathematics

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Explore a collection of the most read and most cited articles making an impact in the Quarterly Journal of Mathematics published within the past two years. This collection will be continuously updated with the journal's leading articles so be sure to revisit periodically to see what is being read and cited.

Also discover the articles being discussed the most on digital media by exploring this Altmetric report pulling the most discussed articles from the past year.

Most cited

On the Rankin–Selberg problem, II

Bingrong Huang

The Quarterly Journal of Mathematics, Volume 75, Issue 1, March 2024, Pages 1–10, https://doi.org/10.1093/qmath/haad037

In this paper, we improve our bounds on the Rankin–Selberg problem. That is, we obtain a smaller error term of the second moment of Fourier coefficients of a GL(2) cusp form (both holomorphic and Maass).

Morse numbers of function germs with isolated singularities

Laurenţiu Maxim and Mihai Tibăr

The Quarterly Journal of Mathematics, Volume 74, Issue 4, December 2023, Pages 1535–1544, https://doi.org/10.1093/qmath/haad033

A set of Morse numbers is associated with a holomorphic function germ with stratified isolated singularity, extending the classical Milnor–Morse number to the setting of a singular base space.

On the Coincidence between Campanato Functions and Lipschitz Functions: A New Approach via Elliptic PDES

Bo Li and others

The Quarterly Journal of Mathematics, Volume 75, Issue 2, June 2024, Pages 663–693, https://doi.org/10.1093/qmath/haae019

Let $({\mathcal{M}},d,\mu)$ be the metric measure space with a Dirichlet form $\mathscr{E}$ . In this paper, we obtain that the Campanato function and the Lipschitz function do always coincide. Our approach is based on the harmonic extension technology, which extends a function u on ${\mathcal{M}}$ to its Poisson integral ...

Motivic Geometry of two-Loop Feynman Integrals

Charles F Doran and others

The Quarterly Journal of Mathematics, Volume 75, Issue 3, September 2024, Pages 901–967, https://doi.org/10.1093/qmath/haae015

We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into mixed Tate pieces and the Hodge structures of families of hyperelliptic, elliptic or rational ...

Exponentially Many Graphs Are Determined By Their Spectrum

Illya Koval and Matthew Kwan

The Quarterly Journal of Mathematics, Volume 75, Issue 3, September 2024, Pages 869–899, https://doi.org/10.1093/qmath/haae030

As a discrete analogue of Kac’s celebrated question on ‘hearing the shape of a drum’ and towards a practical graph isomorphism test, it is of interest to understand which graphs are determined up to isomorphism by their spectrum (of their adjacency matrix). A striking conjecture in this area, due to van Dam and Haemers, is ...

The codegree isomorphism problem for finite simple groups

Nguyen N Hung and Alexander Moretó

The Quarterly Journal of Mathematics, Volume 75, Issue 3, September 2024, Pages 1157–1179, https://doi.org/10.1093/qmath/haae039

We study the codegree isomorphism problem for finite simple groups. In particular, we show that such a group is determined by the codegrees (counting multiplicity) of its irreducible characters. The proof is uniform for all simple groups and only depends on the classification by means of Artin–Tits’ simple order theorem.

Quantitative results of the Romanov type representation functions

Yong-Gao Chen and Yuchen Ding

The Quarterly Journal of Mathematics, Volume 74, Issue 4, December 2023, Pages 1331–1359, https://doi.org/10.1093/qmath/haad022

For α > 0, let $$\mathscr{A}=\{a_1 \lt a_2 \lt a_3\lt\cdots\}$$ and $$\mathscr{L}=\{\ell_1, \ell_2, \ell_3,\cdots\} \quad \text{(not\ necessarily\ different)}$$ be two sequences of positive integers with $\mathscr{A}(m)\gt(\log m)^\alpha $ for infinitely many positive integers m and $\ell_m\lt0.9\log\log m$ for ...

Bounded cohomology and homotopy colimits

George Raptis

The Quarterly Journal of Mathematics, Volume 75, Issue 4, December 2024, Pages 1219–1241, https://doi.org/10.1093/qmath/haae031

The comparison map from bounded cohomology to singular cohomology plays an important role in the study of bounded cohomology theory and its applications. The vanishing and covering theorems of Gromov and Ivanov show interesting and useful properties of the comparison map under appropriate assumptions. We discuss an ...

A Mean Value Theorem for General Dirichlet Series

Frederik Broucke and Titus Hilberdink

The Quarterly Journal of Mathematics, Volume 75, Issue 4, December 2024, Pages 1393–1413, https://doi.org/10.1093/qmath/haae051

In this paper we obtain a mean value theorem for a general Dirichlet series $f(s)= \sum_{j=1}^\infty a_j n_j^{-s}$ with positive coefficients for which the counting function $A(x) = \sum_{n_{j}\le x}a_{j}$ satisfies $A(x)=\rho x + O(x^\beta)$ for some ρ > 0 and β < 1. We prove that $\frac1T\int_0^T ...

Graded Hecke algebras and equivariant constructible sheaves on the nilpotent cone

Maarten Solleveld

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 109–146, https://doi.org/10.1093/qmath/haae065

Graded Hecke algebras can be constructed geometrically, with constructible sheaves and equivariant cohomology. The input consists of a complex reductive group G (possibly disconnected) and a cuspidal local system on a nilpotent orbit for a Levi subgroup of G . We prove that every such “geometric” graded Hecke algebra is ...

Most read

Research Article

Equivariant Deformation theory for Nilpotent slices in Symplectic lie Algebras

Filippo Ambrosio and Lewis Topley

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 47–68, https://doi.org/10.1093/qmath/haae063

The Slodowy slice is a flat Poisson deformation of its nilpotent part, and it was demonstrated by Lehn–Namikawa–Sorger that there is an interesting infinite family of nilpotent orbits in symplectic Lie algebras for which the slice is not the universal Poisson deformation of its nilpotent part. This family corresponds to ...

Research Article

Proper pushforwards on analytic adic spaces

Tomoyuki Abe and Christopher Lazda

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 147–183, https://doi.org/10.1093/qmath/haae066

We construct proper pushforwards for partially proper morphisms of analytic adic spaces. This generalises the theory due to van der Put in the case of rigid analytic varieties over a non-Archimedean field. For morphisms that are smooth and partially proper in the sense of Kiehl, we furthermore construct the trace map and ...

Research Article

Stability conditions in geometric invariant theory

Ruadhaí Dervan and Andrés Ibáñez Núñez

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 287–311, https://doi.org/10.1093/qmath/haae068

We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with a group action and ultimately to a notion of a stability condition on a stack ...

Research Article

The non-commuting, non-generating graph of a finite simple group

Saul D Freedman

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 313–335, https://doi.org/10.1093/qmath/haaf003

Let G be a group such that $G/Z(G)$ is finite and simple. The non-commuting, non-generating graph $\Xi(G)$ of G has vertex set $G \backslash Z(G)$ , with edges corresponding to pairs of elements that do not commute and do not generate G . Complementing our previous investigation of this graph for non-simple groups, we show ...

Research Article

Exponentially Many Graphs Are Determined By Their Spectrum

Illya Koval and Matthew Kwan

The Quarterly Journal of Mathematics, Volume 75, Issue 3, September 2024, Pages 869–899, https://doi.org/10.1093/qmath/haae030

As a discrete analogue of Kac’s celebrated question on ‘hearing the shape of a drum’ and towards a practical graph isomorphism test, it is of interest to understand which graphs are determined up to isomorphism by their spectrum (of their adjacency matrix). A striking conjecture in this area, due to van Dam and Haemers, is ...

Research Article

Sumsets in the set of squares

Christian Elsholtz and Lena Wurzinger

The Quarterly Journal of Mathematics, Volume 75, Issue 4, December 2024, Pages 1243–1254, https://doi.org/10.1093/qmath/haae044

We study sumsets $\mathcal{A}+\mathcal{B}$ in the set of squares $\mathcal{S}$ (and, more generally, in the set of k th powers $\mathcal{S}_k$ , where $k\geq 2$ is an integer). It is known by a result of Gyarmati that $\mathcal{A}+\mathcal{B}\subset \mathcal{S}_k \cap [1,N]$ implies that ...

Research Article

Euler Systems and Selmer Bounds for GU(2,1)

Muhammad Manji

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 217–235, https://doi.org/10.1093/qmath/haae070

We investigate properties of the Euler system associated with certain automorphic representations of the unitary similitude group GU(2,1) with respect to an imaginary quadratic field E , constructed by Loeffler–Skinner–Zerbes. By adapting Mazur and Rubin’s Euler system machinery we prove one divisibility of the ‘rank 1’ ...

Research Article

ALE Spaces and Nodal Curves

Nigel Hitchin

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 337–347, https://doi.org/10.1093/qmath/haaf004

We consider the twistor theory approach to Kronheimer's ALE metrics on the resolution of a Kleinian singularity. The circle action on the 4-manifold induces a C*-action on a compactification of the twistor space and we identify the orbit of a generic twistor line as a nodal rational curve in a particular cohomology class ...

Research Article

Representations on canonical models of generalized fermat curves and their syzygies

Kostas Karagiannis

The Quarterly Journal of Mathematics, Volume 76, Issue 1, March 2025, Pages 95–107, https://doi.org/10.1093/qmath/haae064

We study canonical models of $\left(\mathbb{Z}/k\mathbb{Z}\right)^n$ -covers of the projective line, tamely ramified at exactly n + 1 points each of index k , when $k,n\geq 2$ and the characteristic of the ground field K is either zero or does not divide k . We determine explicitly the structure of the respective ...

Research Article

A Cauchy–Davenport Theorem for Locally Compact Groups

Yifan Jing and Chieu-Minh Tran

The Quarterly Journal of Mathematics, Volume 75, Issue 4, December 2024, Pages 1363–1374, https://doi.org/10.1093/qmath/haae049

We generalize the Cauchy–Davenport theorem to all locally compact groups.