Results 41 to 50 of about 50,891 (201)
Double Shuffle Relations of Double Zeta Values and Double Eisenstein Series of Level N
, 2015 In their seminal paper "Double zeta values and modular forms" Gangl, Kaneko and Zagier defined a double Eisenstein series and used it to study the relations between double zeta values.
Yuan, Haiping, Zhao, Jianqiang
core +1 more source
Sustainable Development, EarlyView.ABSTRACT ‘Hard’ natural sciences have extensively been used to provide evidence that climate change is happening and climate action is needed. If the contribution of our economic activities to disturbing our climate systems is now largely accepted, the way in which we design and operationalise ‘climate action’—how we transition to more sustainable ...
Sandrine Simon
wiley +1 more source
Eisenstein series and convolution sums [PDF]
The Ramanujan Journal, 2018 We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $ \sum_{a+p b=n} (a) (b)$, $ \sum_{p_1a+p_2 b=n} (a) (b)$ and $ \sum_{a+p_1 p_2 b=n} (a) (b)$ where $p, p_1, p_2$ are primes.
openaire +4 more sources
Degenerate Eisenstein Series for $Sp_4$ [PDF]
Journal of number theory, 2013 In this paper we obtain a complete description of images and poles of degenerate Eisenstein series attached to maximal parabolic subgroups of $Sp_4(\mathbb A)$, where $\mathbb A$ is the ring of adeles of $\mathbb Q$.
Hanzer, Marcela, Muić, Goran
openaire +3 more sources
The hidden discount: Examining racial disparity in the use of suspended sentences
Criminology, EarlyView.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 +3 more
wiley +1 more source
Advanced tools for basis decompositions of genus-one string integrals
Journal of High Energy PhysicsIn string theories, one-loop scattering amplitudes are characterized by integrals over genus-one surfaces using the Kronecker-Eisenstein series. A recent methodology proposed a genus-one basis formed from products of these series of chain topologies.
Yong Zhang
doaj +1 more source
On certain relations among the generating functions for certain quadratic forms [PDF]
Notes on Number Theory and Discrete MathematicsThe object of this article is to establish the relation between the generating function of the quadratic form 2m²+2mn+3n² and the generating functions for the quadratic forms m²+mn+n², m²+mn+2n², m²+mn+4n² and 2m²+mn+2n².
K. R. Vasuki, P. Nagendra
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Integrating three-loop modular graph functions and transcendentality of string amplitudes
Journal of High Energy Physics, 2022 Modular graph functions (MGFs) are SL(2, ℤ)-invariant functions on the Poincaré upper half-plane associated with Feynman graphs of a conformal scalar field on a torus.
Eric D’Hoker, Nicholas Geiser
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Whose decision is it anyway? Defendants’ prior experience shapes prosecutorial case dismissal
Criminology, EarlyView.Abstract Studies of early case processing outcomes in the United States typically assume that decisions are made unilaterally by the prosecutor, such that prior contact with the legal system is universally associated with harsher outcomes for defendants.
R. R. Dunlea, Miranda A. Galvin
wiley +1 more source
SciPost Physics, 2022 We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\cN=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$, $SO(2N+1)$, $USp(2N)$.
Daniele Dorigoni, Michael B. Green, Congkao Wen
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