Results 41 to 50 of about 16,023 (137)

Toroidal automorphic forms, Waldspurger periods and double Dirichlet series

, 2011
The space of toroidal automorphic forms was introduced by Zagier in the 1970s: a GL_2-automorphic form is toroidal if it has vanishing constant Fourier coefficients along all embedded non-split tori. The interest in this space stems (amongst others) from
Alain Connes, André Weil, Benji Fisher and Solomon Friedberg, Erich Hecke. Über die Kroneckersche Grenzformel für reelle quadratische Körper und die Klassenzahl relativ-abelscher Körper, Frank Wielonsky, Gautam Chinta and Dorian Goldfeld, Gilles Lachaud, Gunther Cornelissen and Oliver Lorscheid, Jean-Loup Waldspurger, Jean-Loup Waldspurger, Jens Franke, M Ram Murty, Michael Rubinstein, Norbert Klingen, Solomon Friedberg and Jeffrey Hoffstein   +14 more
core   +1 more source

Soft bounds for local triple products and the subconvexity‐QUE implication for GL2$\mathrm{GL}_2$

Mathematika, Volume 71, Issue 4, October 2025.
Abstract We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.
Paul D. Nelson
wiley   +1 more source

Asymptotic behaviors of means of central values of automorphic $L$-functions for GL(2)

, 2014
Let $\mathbb{A}$ be the adele ring of a totally real algebraic number field $F$. We push forward an explicit computation of a relative trace formula for periods of automorphic forms along a split torus in $GL(2)$ from a square free level case done by ...
Sugiyama, Shingo
core   +1 more source

The conjugacy problem for ascending HNN‐extensions of free groups

Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.
Abstract We give an algorithm to solve the Conjugacy Problem for ascending HNN‐extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group endomorphisms.
Alan D. Logan
wiley   +1 more source

Triple Product L Functions and Quantum Chaos on SL(2,C) [PDF]

, 2010
We extend the results of Watson, which link quantum unique ergodicity on arithmetic hyperbolic surfaces with subconvexity for the triple product L function, to the case of arithmetic hyperbolic three manifolds.
Marshall, Simon
core  

Bagchi's Theorem for families of automorphic forms

, 2017
We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem for family of primitive cusp forms of weight $2$ and prime level, and discuss under which conditions the argument will apply to general reasonable family of automorphic $L ...
A. Laurinčikas, B. Conrey, D. Li, E. Kowalski, E. Kowalski, E. Kowalski, E.C. Titchmarsh, J. Cogdell, J.-P. Serre, J.B. Conrey, P. Billingsley, P. Sarnak   +11 more
core   +1 more source

Correlations of the squares of the Riemann zeta function on the critical line

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract We compute the average of a product of two shifted squares of the Riemann zeta function on the critical line with shifts up to size T3/2−ε$T^{3/2-\varepsilon }$. We give an explicit expression for such an average and derive an approximate spectral expansion for the error term similar to Motohashi's.
Valeriya Kovaleva
wiley   +1 more source

The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms

Forum of Mathematics, Pi
We prove the Ramanujan and Sato–Tate conjectures for Bianchi modular forms of weight at least $2$ . More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of $\operatorname {\mathrm {GL}}_2 ...
George Boxer, Frank Calegari, Toby Gee, James Newton, Jack A. Thorne   +4 more
doaj   +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, Morten S. Risager, Igor E. Shparlinski   +2 more
wiley   +1 more source

A decomposition of the Fourier-Jacobi coefficients of Klingen Eisenstein series [PDF]

, 2017
We investigate the relation between Klingen's decomposition of the space of Siegel modular forms and Dulinski's analogous decomposition of the space of Jacobi forms.Comment: Summary of a talk at the RIMS workshop "Automorphic Forms and Related Topics",
Paul, Thorsten, Schulze-Pillot, Rainer
core   +1 more source