Results 61 to 70 of about 1,658 (186)

Spatial Heterogeneity in Climate Risk and Human Flourishing: An Exploration With Generative AI

Transactions in GIS, Volume 30, Issue 4, June 2026.
ABSTRACT Recent advances in generative Artificial Intelligence (AI), particularly Large Language Models (LLMs), enable scalable extraction of spatial information from unstructured text and offer new methodological opportunities for studying climate geography.
Stefano M. Iacus, Haodong Qi, Devika Jain   +2 more
wiley   +1 more source

MODULI INTERPRETATION OF EISENSTEIN SERIES [PDF]

International Journal of Number Theory, 2012
Let ℓ ≥ 3. Using the moduli interpretation, we define certain elliptic modular forms of level Γ(ℓ) over any field k where 6ℓ is invertible and k contains the ℓth roots of unity. These forms generate a graded algebra [Formula: see text], which, over C, is generated by the Eisenstein series of weight 1 on Γ(ℓ).
openaire   +3 more sources

On p-adic quaternionic Eisenstein series [PDF]

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2013
We show that certain $p$-adic Eisenstein series for quaternionic modular groups of degree 2 become "real" modular forms of level $p$ in almost all cases. To prove this, we introduce a $U(p)$ type operator. We also show that there exists a $p$-adic Eisenstein series of the above type that has transcendental coefficients.
Kikuta, Toshiyuki, Nagaoka, Shoyu
openaire   +2 more sources

Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52

Open Mathematics, 2017
The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
doaj   +1 more source

Non-holomorphic modular forms from zeta generators

Journal of High Energy Physics
We study non-holomorphic modular forms built from iterated integrals of holomorphic modular forms for SL(2, ℤ) known as equivariant iterated Eisenstein integrals.
Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Oliver Schlotterer, Leila Schneps, Bram Verbeek   +7 more
doaj   +1 more source

Fourier expansions of complex-valued Eisenstein series on finite upper half planes

International Journal of Mathematics and Mathematical Sciences, 2006
We consider complex-valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp).
Anthony Shaheen, Audrey Terras
doaj   +1 more source

The hidden discount: Examining racial disparity in the use of suspended sentences

Criminology, Volume 64, Issue 2, Page 450-484, May 2026.
Abstract Extant research on criminal sentencing generally concludes that racial/ethnic disparity is concentrated in the “in–out” decision, and that racial differences in sentence lengths are small and inconsistent. However, sentence length analyses rarely focus on the fact that criminal sentences are often partially or fully suspended, creating ...
Kevin Petersen, Brian D. Johnson, Allison D. Redlich, Miranda A. Galvin   +3 more
wiley   +1 more source

Eisenstein series and approximations to $\pi$

Illinois Journal of Mathematics, 2001
The first purpose of this paper is to elucidate some marginal notes of Ramanujan found in his ``lost notebook''. It turns out that these notes give relations between certain values of \(Q^3\) and \(R^2\) where \(Q\) and \(R\) are Ramanujan's usual notations for the Eisenstein series of weight 4 and 6.
Berndt, Bruce C., Chan, Heng Huat
openaire   +3 more sources

The impact of prosecutors’ office caseloads on case processing outcomes

Criminology &Public Policy, Volume 25, Issue 2, Page 297-322, May 2026.
Research Summary Contemporary criminal justice discourse frequently highlights rising caseloads as a crisis for prosecutors across the United States. Yet, empirical assessments of how caseloads impact prosecutorial decision making are scarce. This study exploits data on office caseloads and cases disposed between 2021 and 2024 in 19 prosecutors ...
R. R. Dunlea, Don Stemen
wiley   +1 more source

Hankel Determinants of Eisenstein Series [PDF]

, 2001
In this paper we prove Garvan's conjectured formula for the square of the modular discriminant $Δ$ as a 3 by 3 Hankel determinant of classical Eisenstein series $E_{2n}$. We then obtain similar formulas involving minors of Hankel determinants for $E_{2r}Δ^m$, for $m=1,2,3$ and $r=2,3,4,5,7$, and $E_{14}Δ^4$.
openaire   +2 more sources