scholarly journals Points whose coordinates are logarithms of algebraic numbers on algebraic varieties

1995 ◽  
Vol 175 (1) ◽  
pp. 49-73 ◽  
Author(s):  
Damien Roy
Keyword(s):  
Algebraic Varieties ◽  
Algebraic Numbers

scholarly journals A PSEUDOEXPONENTIAL-LIKE STRUCTURE ON THE ALGEBRAIC NUMBERS

2015 ◽  
Vol 80 (4) ◽  
pp. 1339-1347
Author(s):  
VINCENZO MANTOVA
Keyword(s):  
Algebraic Varieties ◽  
Algebraic Numbers ◽  
Exponential Functions ◽  
Existentially Closed ◽  
Existential Closure ◽  
Independent Functions ◽  
Schanuel's Conjecture

AbstractPseudoexponential fields are exponential fields similar to complex exponentiation which satisfy the Schanuel Property, i.e., the abstract statement of Schanuel’s Conjecture, and an adapted form of existential closure.Here we show that if we remove the Schanuel Property and just care about existential closure, it is possible to create several existentially closed exponential functions on the algebraic numbers that still have similarities with complex exponentiation. The main difficulties are related to the arithmetic of algebraic numbers, and they can be overcome with known results about specialisations of multiplicatively independent functions on algebraic varieties.

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Recent Work ◽  
Chow Groups ◽  
Ring Structure ◽  
Complete Intersections ◽  
Algebraic Varieties ◽  
Chow Ring ◽  
Hodge Structures ◽  
Chow Rings ◽  
Geometric Methods ◽  
The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS

2010 ◽  
Vol 06 (01) ◽  
pp. 69-87 ◽  
Author(s):  
ALISON MILLER ◽  
AARON PIXTON
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Algebraic Numbers ◽  
Heegner Points ◽  
Positive Weight ◽  
Poincare Series ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Modular Invariants

We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].

scholarly journals Zero-Sum Stochastic Games over the Field of Real Algebraic Numbers

2019 ◽  
Vol 9 (4) ◽  
pp. 1026-1041
Author(s):  
K. Avrachenkov ◽  
V. Ejov ◽  
J. A. Filar ◽  
A. Moghaddam
Keyword(s):  
Stochastic Games ◽  
Algebraic Numbers ◽  
Zero Sum
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