H. Grobner

activity

20102026

most citedWhittaker periods, motivic periods, and special values of tensor product L-functions

20 citations · 49 across the 11 of their papers we have counts for

collaborators

12 papers

math.NT2026

On divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting function

Harald Grobner

An explicit formula for the prime-counting function $π (x)$ , usually attributed to Riemann and von Mangoldt, is prominently stated as the equation $π (x) = R (x) - \sum_{ρ} R (x^{ρ})$ , where th…

math.NT2026

On the residual Eisenstein cohomology of unitary groups

Harald Grobner

We investigate the residual Eisenstein cohomology of an arbitrary unitary group $U (V)$ attached to an arbitrary quadratic extension of number fields $E / F$ . Our focus lies on the co…

math.LO2026

Uniformity of Consistency in Arithmetic and Gödel's Second Incompleteness Theorem: Ein Märchen

Harald Grobner

In much discussed work Artemov has recently argued that, for $PA$ , the consistency schema admits a form of uniform verification via selector-proofs, despite the unprovabil…

math.NT2025

Factorization of periods, construction of automorphic motives and Deligne's conjecture over CM-fields

Harald Grobner, Michael Harris, Jie Lin

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$ -functions and the multiplicative relations between periods of arithmeti…

math.NT2021

On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations

Harald Grobner, Sonja Žunar

In this paper we describe several new aspects of the foundations of the representation theory of the space of smooth-automorphic forms (i.e., not necessarily $K_{\infty}$ -finite auto…

math.NT2018★ 3 cited

Deligne's conjecture for automorphic motives over CM-fields

Harald Grobner, Michael Harris, Jie Lin

The present paper is devoted to the relations between Deligne's conjecture on critical values of motivic $L$ -functions and the multiplicative relations between periods of arithmeti…

math.NT2017★ 1 cited

Special values of $L$ -functions and the refined Gan-Gross-Prasad conjecture

Harald Grobner, Jie Lin

We prove explicit rationality-results for Asai- $L$ -functions, $L^{S} (s, Π^{'}, As^{\pm})$ , and Rankin-Selberg $L$ -functions, $L^{S} (s, Π \times Π^{'})$ , over arbitrary CM-fields $F$ , relatin…

math.NT2014

A rationality result for the exterior and the symmetric square $L$ -function

Harald Grobner

Let $G = GL_{2 n}$ over a totally real number field $F$ and $n \geq 2$ . Let $Π$ be a cuspidal automorphic representation of $G (A)$ , which is cohomological and a functoria…

math.NT2014★ 17 cited

Whittaker rational structures and special values of the Asai $L$ -function

Harald Grobner, Michael Harris, Erez Lapid

Let $F$ be a totally real number field and $E / F$ a totally imaginary quadratic extension of $F$ . Let $Π$ be a cohomological, conjugate self-dual cuspidal automorphic representation…

math.NT2013★ 20 cited

Whittaker periods, motivic periods, and special values of tensor product L-functions

Harald Grobner, Michael Harris

Let $K$ be an imaginary quadratic field. Let $Π$ and $Π^{'}$ be irreducible generic cohomological automorphic representation of $G L (n) / K$ and $GL(n-1)/{\mathcal K}…

math.NT2011★ 3 cited

On the arithmetic of Shalika models and the critical values of $L$ -functions for $GL (2 n)$

Harald Grobner, A. Raghuram

Let $Π$ be a cohomological cuspidal automorphic representation of $GL_{2 n} (A)$ over a totally real number field $F$ . Suppose that $Π$ has a Shalika model. We define a…

math.NT2010★ 5 cited

Automorphic Forms, Cohomology and CAP Representations. The Case $G L_{2}$ over a definite quaternion algebra

Harald Grobner

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G = G L_{2}$ over a definite quaternion algebra $D/\Q$. Functoriality is used to show the existe…

On divergence related to Riemann--von Mangoldt's explicit formula of the prime-counting function

On the residual Eisenstein cohomology of unitary groups

Uniformity of Consistency in Arithmetic and Gödel's Second Incompleteness Theorem: Ein Märchen

Factorization of periods, construction of automorphic motives and Deligne's conjecture over CM-fields

On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations

Deligne's conjecture for automorphic motives over CM-fields

Special values of L-functions and the refined Gan-Gross-Prasad conjecture

A rationality result for the exterior and the symmetric square L-function

Whittaker rational structures and special values of the Asai L-function

Whittaker periods, motivic periods, and special values of tensor product L-functions

On the arithmetic of Shalika models and the critical values of L-functions for GL(2n)

Automorphic Forms, Cohomology and CAP Representations. The Case GL2​ over a definite quaternion algebra

Special values of $L$ -functions and the refined Gan-Gross-Prasad conjecture

A rationality result for the exterior and the symmetric square $L$ -function

Whittaker rational structures and special values of the Asai $L$ -function

On the arithmetic of Shalika models and the critical values of $L$ -functions for $GL (2 n)$

Automorphic Forms, Cohomology and CAP Representations. The Case $G L_{2}$ over a definite quaternion algebra