324,391 research outputs found
Weil's converse theorem for Maass forms and cancellation of zeros
Get PDFWe prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass newform and the Riemann zeta function has infinitely many poles
Preprint: Weil's Converse Theorem for Maass Forms and Cancellation of Zeros
No full textWe prove two principal results. Firstly, we characterise Maass forms in terms of functional equations for Dirichlet series twisted by primitive characters. The key point is that the twists are allowed to be meromorphic. This weakened analytic assumption applies in the context of our second theorem, which shows that the quotient of the symmetric square L-function of a Maass newform and the Riemann zeta function has infinitely many poles
Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow
No full textBy a transfer operator approach to Maass cusp forms and the Selberg zeta function for cofinite Hecke triangle groups, Moller and the present author found a factorization of the Selberg zeta function into a product of Fredholm determinants of transfer-operator-like families: Z(s) = det(1 - L-s(+)) det(1 - L-s(-)). In this article we show that the operator families L-s(+/-) arise as families of transfer operators for the triangle groups underlying the Hecke triangle groups, and that for s is an element of C, Res = 1/2, the operator L-s(+) (respectively L-s(-)) has a 1-eigenfunction if and only if there exists an even (respectively odd) Maass cusp form with eigenvalue s(1 - s). For non-arithmetic Hecke triangle groups, this result provides a new formulation of the Phillips-Sarnak conjecture on non-existence of even Maass cusp forms.Volkswagen Foundatio
Period functions for vector-valued Maass cusp forms of real weight, with an application to Jacobi Maass cusp forms
Get PDFFor vector-valued Maass cusp forms for~ with real weight~ and spectral parameter , , mod , we propose a notion of vector-valued period functions, and we establish a linear isomorphism between the spaces of Maass cusp forms and period functions by means of a cohomological approach. The period functions are a generalization of those for the classical Maass cusp forms, being solutions of a finite-term functional equation or, equivalently, eigenfunctions with eigenvalue of a transfer operator deduced from the geodesic flow on the modular surface. We apply this result to deduce a notion of period functions and related linear isomorphism for Jacobi Maass forms of weight for the semi-direct product of with the integer points of the Heisenberg group.58 pages, 7 figur
A Burgess-like subconvex bound for twisted L-functions
Get PDFLet g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, X a primitive character of conductor q, and s a point on the critical line Rs = 1/2. It is proved that
L(g circle times chi, s) 0
is arbitrary and theta = 7/64 is the current known approximation towards the RamannJan-Petersson conjecture (which would allow theta = 0); moreover, the dependence on s and all the parameters of g is polynomial. This result is an analog of Burgess' classical subconvex bound for Dirichlet L-functions. In Appendix 2 the above result is combined with a theorem of Waldspurger and the adelic calculations of Baruch-Mao to yield an improved uniform upper bound for the Fourier coefficients of holomorphic half-integral weight cusp forms
The cultural context of biodiversity conservation
Get PDFSoftcover, 303 S.: 38,00 €Softcover, 17x24How are biological diversity, protected areas, indigenous knowledge and religious worldviews related? From an anthropological perspective, this book provides an introduction into the complex subject of conservation policies that cannot be addressed without recognising the encompassing relationship between discursive, political, economic, social and ecological facets. By facing these interdependencies across global, national and local dynamics, it draws on an ethnographic case study among Maya-Q'eqchi' communities living in the margins of protected areas in Guatemala. In documenting the cultural aspects of landscape, the study explores the coherence of diverse expressions of indigenous knowledge. It intends to remind of cultural values and beliefs closely tied to subsistence activities and ritual practices that define local perceptions of the natural environment. The basic idea is to illustrate that there are different ways of knowing and reasoning, seeing and endowing the world with meaning, which include visible material and invisible interpretative understandings. These tend to be underestimated issues in international debates and may provide an alternative approach upon which conservation initiatives responsive to the needs of the humans involved should be based on
On Fourier coefficients of Maass waveforms for 𝑃𝑆𝐿(2,𝑍)
No full textIn this paper, we use machine experiments to test the validity of the Sato-Tate conjecture for Maass waveforms on
P
S
L
(
2
,
m
a
t
h
b
b
Z
)
∖
H
\mathrm {PSL}(2,\ mathbb{Z})\backslash H
. We also elaborate on Stark’s iterative method for calculating the Fourier coefficients of such forms.</p
On the sup-norm of Maass cusp forms of large level: II
No full textLet f be a Hecke-Maass cuspidal newform of square-free level N and Laplacian eigenvalue λ. It is shown that for any ε>0, with an implied constant depending continuously on λ. The proof is short and self-contained. © 2011 The Author(s). Published by Oxford University Press. All rights reserved
Twisted traces of CM values of weak Maass forms
No full textAlfes C, Ehlen S. Twisted traces of CM values of weak Maass forms. Journal of Number Theory. 2013;133(6):1827-1845
Asymptotic densities of Maass newforms
No full textAbstractWe define the counting function for Maass newforms of Hecke congruence groups and calculate the three main terms of this counting function. We then give necessary and sufficient conditions for this expansion to have the same shape as if it were counting eigenvalues related to cocompact surfaces. We relate the result to classical instances of the Jacquet–Langlands correspondence
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