A certain Dirichlet series attached to Siegel modular forms of degree two.
A converse theorem for second-order modular forms of level N
A Dirichlet series for Hermitian modular forms of degree 2
A Dirichlet series for modular forms of degree n
A mean square formula for central values of twisted automorphic L-functions
A new multiple Dirichlet series induced by a higher-order form
A note on average behaviour of the Fourier coefficients of th symmetric power -function over certain sparse sequence of positive integers
Let be a given integer. Let be the set of all normalized primitive holomorphic cusp forms of even integral weight for the full modulo group . For , denote by the th normalized Fourier coefficient of th symmetric power -function () attached to . We are interested in the average behaviour of the sum where is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023).
A Rankin-Selberg integral for the adjoint representation of GL3.
A remark on Construire un noyau de la fonctorialité by Lafforgue
Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic extension. For technical reasons, he considers only the case of function fields and assumes the data is unramified. In this paper, we show that his method applies without these restrictions. The ground field is a number field or a function field and the data may be ramified.
Abelova cena v roce 2018 udělena za Langlandsův program
V článku motivujeme a vysvětlíme základy Langlandsova programu, sítě domněnek propojujících řadu různých oblastí matematiky. Během toho se také setkáme s Riemannovou hypotézou a domněnkou Birche a Swinnerton-Dyera, dvěma ze sedmi problémů tisíciletí vyhlášených Clayovým matematickým institutem.
Action of Hecke operators on products of Igusa theta constants with rational characteristics
Admissible -adic measures attached to triple products of elliptic cusp forms.
An application of the projections of automorphic forms
An orthogonal test of the L-functions Ratios Conjecture, II
Andrianov' s L-functions associated to Siegel wave forms of degree two.
Artin formalism and heat kernels.
Automorphic -functions in the weight aspect.
Bounds for automorphic L-functions.
Bounds for automorphic L-functions. II.
Bounds for modular L-functions in the level aspect