Let F be a nonarchimedean local field of residual characteristic p≠2. G (connected) reductive group that splits over tamely ramified extension F. We show construction analogous to Yu’s complex supercuspidal representations yields smooth, irreducible, cuspidal an arbitrary algebraically closed R different from p. Moreover, we prove this provides all R-representations if p does not divide the ord...

We make the subconvex exponent for GL2 cuspidal representation in work of Michel & Venkatesh explicit. The result depends on an effective dependence “fixed” our former bounds twists by Hecke characters, which turn L4-norm test function.

‎The Mod $2$ Steenrod algebra is a Hopf algebra that consists of the primary cohomology operations‎, ‎denoted by $Sq^n$‎, ‎between the cohomology groups with $mathbb{Z}_2$ coefficients of any topological space‎. ‎Regarding to its vector space structure over $mathbb{Z}_2$‎, ‎it has many base systems and some of the base systems can also be restricted to its sub algebras‎. ‎On the contrary‎, ‎in ...

We show entireness of complete adjoint L-functions associated to any cuspidal representations $${{\,\mathrm{GL}\,}}(3)$$ or $${{\,\mathrm{GL}\,}}(4)$$ over an arbitrary number field. Twisted cases are also investigated.

We compute the Euler characteristics of the moduli spaces of abelian vortices on curves with nodal and cuspidal singularities. This generalizes our previous work where only nodes were taken into account. The result we obtain is again consistent with the expected reconciliation between the vortex picture of D2-D0 branes and the proposal by Gopakumar and Vafa.

Let L(s, π) be the principal L-function attached to an irreducible unitary cuspidal automorphic representation π of GLm(AQ). The aim of the paper is to give a simple method to show the lower bounds of mean value for automorphic L-functions over short intervals.

For automorphic representations in the nontempered cuspidal spectrum of SO5, we establish a precise Bessel period formula, in which the square of the global Bessel period is decomposed as an Euler product of regularized local Bessel period integrals of matrix coefficients.

We will show a theorem of a type of Cheeger and Müller for a non-compact complete hyperbolic threefold of finite volume. As an application we will compute a special value of Ruelle L-function at the origin for a unitary local system which is cuspidal.