Results 81 to 90 of about 3,473,158 (260)

Character sum, reciprocity, and Voronoi formula

Bulletin of the London Mathematical Society, EarlyView.
Abstract We prove a novel four‐variable character sum identity that serves as a twisted, non‐Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists.
Chung‐Hang Kwan, Wing Hong Leung
wiley   +1 more source

Advanced tools for basis decompositions of genus-one string integrals

Journal of High Energy Physics
In 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

Exact results for duality-covariant integrated correlators in $\mathcal{N}=4$ SYM with general classical gauge groups

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
doaj   +1 more source

On Eisenstein Series of GLn

Journal of Number Theory, 1995
Since the results are very technical it is difficult to state them here explicitly and so we quote from the author's introduction: ``In this paper we present a new method of obtaining an analytic continuation and explicit functional equation for an Eisenstein series attached to any standard maximal parabolic subgroup of \(GL_ n\). One main idea of this
openaire   +3 more sources

Congruences with Eisenstein series and -invariants [PDF]

Compositio Mathematica, 2019
We study the variation of$\unicode[STIX]{x1D707}$-invariants in Hida families with residually reducible Galois representations. We prove a lower bound for these invariants which is often expressible in terms of the$p$-adic zeta function. This lower bound forces these$\unicode[STIX]{x1D707}$-invariants to be unbounded along the family, and we conjecture
Bellaïche, Joël, Pollack, Robert
openaire   +6 more sources

Mapping Family Policy Developments in 45 Western and Latin American Countries Over 120 Years: A Global Political Economy Interpretation

Social Policy &Administration, Volume 59, Issue 6, Page 994-1014, November 2025.
ABSTRACT We map explicit family policy evolution across 45 Western and Latin American countries over 120 years, analysing policy developments in child‐related leaves, child benefits, CCTs, and ECEC. Using a newly created dataset, we advance the literature in two ways.
Tobias Böger, Barbara Zárate‐Tenorio, Emanuele Ferragina   +2 more
wiley   +1 more source

On certain relations among the generating functions for certain quadratic forms [PDF]

Notes on Number Theory and Discrete Mathematics
The 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
doaj   +1 more source

Soft bounds for local triple products and the subconvexity‐QUE implication for GL2$\mathrm{GL}_2$

Mathematika, Volume 71, Issue 4, October 2025.
Abstract We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.
Paul D. Nelson
wiley   +1 more source

ZEROS OF EISENSTEIN SERIES

Kyushu Journal of Mathematics, 2004
Let \(E_k\) be the normalized Eisenstein series of weight \(k\) with respect to the modular group \(\Gamma= \text{SL}_2(\mathbb{Z})\). It was shown by \textit{F. K. C. Rankin} and \textit{H. P. F. Swinnerton-Dyer} [Bull. Lond. Math. Soc. 2, 169--170 (1970; Zbl 0203.35504)] that all the zeros of \(E_k\) in the standard fundamental domain \({\mathcal F}\)
openaire   +4 more sources

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