Results 61 to 70 of about 156 (139)
Dirac–Schrödinger operators, index theory and spectral flow
Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.Abstract In this article, we study generalised Dirac–Schrödinger operators in arbitrary signatures (with or without gradings), providing a general KK$\textnormal {KK}$‐theoretic framework for the study of index pairings and spectral flow. We provide a general Callias Theorem, which shows that the index (or the spectral flow, or abstractly the K ...
Koen van den Dungen
wiley +1 more source
Taking limits in topological recursion
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract When does topological recursion applied to a family of spectral curves commute with taking limits? This problem is subtle, especially when the ramification structure of the spectral curve changes at the limit point. We provide sufficient (straightforward‐to‐use) conditions for checking when the commutation with limits holds, thereby closing a ...
Gaëtan Borot +4 more
wiley +1 more source
Galois representations for holomorphic Siegel modular forms
, 2013 We prove local–global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert–Siegel modular forms in many cases (induced from Borel or Klingen parabolic), and as a corollary we obtain a conjecture of Skinner ...
Jorza, Andrei
core
Rankin-Selberg methods for closed string amplitudes
, 2014 After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus $h\leq 3$ are reduced to an integral of a Siegel modular function of degree $h$ on a fundamental domain of the Siegel upper half plane.
Pioline, Boris, Boris Pioline
core +1 more source
Triple sums of Kloosterman sums and the discrepancy of modular inverses
Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.Abstract We investigate the distribution of modular inverses modulo positive integers c$c$ in a large interval. We provide upper and lower bounds for their box, ball, and isotropic discrepancy, thereby exhibiting some deviations from random point sets. The analysis is based, among other things, on a new bound for a triple sum of Kloosterman sums.
Valentin Blomer +2 more
wiley +1 more source
Log-concavity for unimodal sequences
, 2023 In this paper, we prove that the number of unimodal sequences of size $n$ is log-concave. These are coefficients of a mixed false modular form and have a Rademacher-type exact formula due to recent work of the second author and Nazaroglu on false theta ...
Bridges, Walter, Bringmann, Kathrin
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Hecke operators for weakly holomorphic modular forms and supersingular congruences [PDF]
Proceedings of the American Mathematical Society, 2008 We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.
openaire +2 more sources
Quantum geometry and mock modularity
, 2023 In previous work, we used new mathematical relations between Gopakumar-Vafa (GV) invariants and rank 0 Donaldson-Thomas (DT) invariants to determine the first few terms in the generating series of Abelian D4-D2-D0 indices for a class of compact one ...
Pioline, Boris +3 more
core
Zagier duality and integrality of Fourier coefficients for weakly holomorphic modular forms
Journal of Number Theory, 2015 Worked out the isomorphisms for a general sign vector; proved Zagier duality for canonical bases; raise a question on integrality; 24 ...
openaire +2 more sources
, 2012 Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012We present a proof of certain congruences modulo powers of an odd prime for the coefficients of a series produced by repeated application of U -operator to a certain weakly holomorphic ...
Chi, Mingjing
core