Results 31 to 40 of about 8,516 (148)
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
Automorphic Black Holes as Probes of Extra Dimensions
, 2011 Recent progress in the understanding of the statistical nature of black hole entropy shows that the counting functions in certain classes of models are determined by automorphic forms of higher rank. In this paper we combine these results with Langlands'
Cassella, Kayleigh, Schimmrigk, Rolf
core +1 more source
Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
wiley +1 more source
Lp$L^p$‐norm bounds for automorphic forms via spectral reciprocity
Proceedings of the London Mathematical Society, Volume 130, Issue 6, June 2025.Abstract Let g$g$ be a Hecke–Maaß cusp form on the modular surface SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$, namely an L2$L^2$‐normalised non‐constant Laplacian eigenfunction on SL2(Z)∖H$\operatorname{SL}_2(\mathbb {Z}) \backslash \mathbb {H}$ that is additionally a joint eigenfunction of every Hecke operator. We prove the L4$L^
Peter Humphries, Rizwanur Khan
wiley +1 more source
Multiplicity one for certain paramodular forms of genus two
, 2017 We show that certain paramodular cuspidal automorphic irreducible representations of $\mathrm{GSp}(4,\mathbb{A}_\mathbb{Q})$, which are not CAP, are globally generic.
Rösner, Mirko, Weissauer, Rainer
core +1 more source
Arithmetic Satake compactifications and algebraic Drinfeld modular forms
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract In this article, we construct the arithmetic Satake compactification of the Drinfeld moduli schemes of arbitrary rank over the ring of integers of any global function field away from the level structure, and show that the universal family extends uniquely to a generalized Drinfeld module over the compactification.
Urs Hartl, Chia‐Fu Yu
wiley +1 more source
L${L}$‐functions of Kloosterman sheaves
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract In this article, we study a family of motives Mn+1k$\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1$n=1$, the L$L$‐functions of M2k$\mathrm{M}_{2}^k$ extend meromorphically to C$\mathbb {C}$ and satisfy the functional equations conjectured by ...
Yichen Qin
wiley +1 more source
Octonionic Magical Supergravity, Niemeier Lattices, and Exceptional & Hilbert Modular Forms
Fortschritte der Physik, Volume 72, Issue 2, February 2024.Abstract The quantum degeneracies of Bogomolny‐Prasad‐Sommerfield (BPS) black holes of octonionic magical supergravity in five dimensions are studied. Quantum degeneracy is defined purely number theoretically as the number of distinct states in charge space with a given set of invariant labels.
Murat Günaydin, Abhiram Kidambi
wiley +1 more source
Remarks on the symmetric powers of cusp forms on GL(2) [PDF]
, 2009 In this paper we prove the following conditional result: Let F be a number field, and pi a cusp form on GL(2)/F which is not solvable polyhedral. Assume that all the symmetric powers sym^m(pi) are modular, i.e., define automorphic forms on GL(m+1)/F.
Ramakrishnan, Dinakar
core +1 more source
A p$p$‐adic approach to the existence of level‐raising congruences
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.Abstract We construct level‐raising congruences between p$p$‐ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the nth$n\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer n=1,3,⋯,25$n =
Jack A. Thorne
wiley +1 more source