scholarly journals Harmonic Eisenstein Series of Weight One

2017 ◽  
pp. 171-184
Author(s):  
Yingkun Li
Keyword(s):  
Eisenstein Series ◽  
Weight One

The dimension of the space of Siegel–Eisenstein series of weight one

2007 ◽  
Vol 260 (1) ◽  
pp. 187-201 ◽  
Author(s):  
Keiichi Gunji
Keyword(s):  
Eisenstein Series ◽  
Weight One

scholarly journals On Wronskians of weight one Eisenstein series

2006 ◽  
Vol 121 (1) ◽  
pp. 132-152
Author(s):  
Lev A. Borisov
Keyword(s):  
Eisenstein Series ◽  
Weight One

scholarly journals Double Dirichlet series and quantum unique ergodicity of weight one-half Eisenstein series

2014 ◽  
Vol 8 (7) ◽  
pp. 1539-1595 ◽  
Author(s):  
Yiannis Petridis ◽  
Nicole Raulf ◽  
Morten Risager
Keyword(s):  
Dirichlet Series ◽  
Eisenstein Series ◽  
Unique Ergodicity ◽  
Double Dirichlet Series ◽  
Weight One

Green function, Painlevé VI equation, and Eisenstein series of weight one

2018 ◽  
Vol 108 (2) ◽  
pp. 185-241 ◽  
Author(s):  
Zhijie Chen ◽  
Ting-Jung Kuo ◽  
Chang-Shou Lin ◽  
Chin-Lung Wang
Keyword(s):  
Green Function ◽  
Eisenstein Series ◽  
Painlevé Vi Equation ◽  
Weight One

Central Histamine, the H3-Receptor and Obesity Therapy

2019 ◽  
Vol 18 (7) ◽  
pp. 516-522
Author(s):  
Néstor F. Díaz ◽  
Héctor Flores-Herrera ◽  
Guadalupe García-López ◽  
Anayansi Molina-Hernández
Keyword(s):  
Body Weight ◽  
Food Intake ◽  
Animal Studies ◽  
Energy Homeostasis ◽  
Receptor Activation ◽  
Receptor Ligands ◽  
Histaminergic System ◽  
H3 Receptor ◽  
Weight One ◽  
The Central Nervous System

The brain histaminergic system plays a pivotal role in energy homeostasis, through H1- receptor activation, it increases the hypothalamic release of histamine that decreases food intake and reduces body weight. One way to increase the release of hypothalamic histamine is through the use of antagonist/inverse agonist for the H3-receptor. Histamine H3-receptors are auto-receptors and heteroreceptors located on the presynaptic membranes and cell soma of neurons, where they negatively regulate the synthesis and release of histamine and other neurotransmitters in the central nervous system. Although several compounds acting as H3-receptor antagonist/inverse agonists have been developed, conflicting results have been reported and only one has been tested as anti-obesity in humans. Animal studies revealed the opposite effect in food intake, energy expeditor, and body weight, depending on the drug, spice, and route of administration, among others. The present review will explore the state of art on the effects of H3-receptor ligands on appetite and body-weight, going through the following: a brief overview of the circuit involved in the control of food intake and energy homeostasis, the participation of the histaminergic system in food intake and body weight, and the H3-receptor as a potential therapeutic target for obesity.

EVALUATION OF CONVOLUTION SUMS AND FOR k = a · b = 21, 33, AND 35

2021 ◽  
pp. 1-20
Author(s):  
K. PUSHPA ◽  
K. R. VASUKI
Keyword(s):  
Positive Integer ◽  
Quadratic Form ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Divisor Function ◽  
Convolution Sums

Abstract The article focuses on the evaluation of convolution sums $${W_k}(n): = \mathop \sum \nolimits_{_{m < {n \over k}}} \sigma (m)\sigma (n - km)$$ involving the sum of divisor function $$\sigma (n)$$ for k =21, 33, and 35. In this article, our aim is to obtain certain Eisenstein series of level 21 and use them to evaluate the convolution sums for level 21. We also make use of the existing Eisenstein series identities for level 33 and 35 in evaluating the convolution sums for level 33 and 35. Most of the convolution sums were evaluated using the theory of modular forms, whereas we have devised a technique which is free from the theory of modular forms. As an application, we determine a formula for the number of representations of a positive integer n by the octonary quadratic form $$(x_1^2 + {x_1}{x_2} + ax_2^2 + x_3^2 + {x_3}{x_4} + ax_4^2) + b(x_5^2 + {x_5}{x_6} + ax_6^2 + x_7^2 + {x_7}{x_8} + ax_8^2)$$ , for (a, b)=(1, 7), (1, 11), (2, 3), and (2, 5).

scholarly journals Tropical ideals do not realise all Bergman fans

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Jan Draisma ◽  
Felipe Rincón
Keyword(s):  
Tropical Geometry ◽  
Tensor Products ◽  
Tropical Variety ◽  
Polyhedral Complex ◽  
Direct Sum ◽  
Weight One ◽  
Polyhedral Complexes

AbstractEvery tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

scholarly journals New modular invariants in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Eisenstein Series ◽  
Mass Parameter ◽  
Flat Space ◽  
Superstring Theory ◽  
Modular Invariant ◽  
Yang Mills ◽  
Laplace Eigenvalue ◽  
Modular Invariants ◽  
Tensor Multiplet ◽  
Super Yang Mills Theory

Abstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ,$$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.

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