相关论文: Class Fields of Complex Multiplication: translatio…
This is the text of an article that I wrote and disseminated in September 1981, except that I've updated the references, corrected a few misprints, and added a table of contents, some footnotes, and an addendum. The original article gave a…
This is an English translation of Felix Klein's paper "Ueber die Transformation elfter Ordnung der elliptischen Functionen" from 1879.
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
This is an appendix to the English translation of the book by A. A. Goldberg and I. V. Ostrovskii, Distribution of values of meromorphic functions, Moscow, Nauka, 1970. An English translation of this book is to be published soon by the AMS.…
Let $K$ be a quartic CM field, that is, a totally imaginary quadratic extension of a real quadratic number field. In a 1962 article titled On the classfields obtained by complex multiplication of abelian varieties, Shimura considered a…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
This is a translation of Kronecker's "\"Uber die Gleichungen f\"unften Grades" (On equations of fifth degree), excerpted from the monthly report to the Berlin Academy of Sciences from June 1861.
In this arxiv-post I present my solutions (published or not) to Problems that appeared in Amer. Math. Monthly, Math. Magazine, Elemente der Mathematik and CRUX, that were mostly done in collaboration with Rudolf Rupp. Some of them…
This collection of problems and conjectures is based on a subset of the open problems from the seminar series and the problem sessions of the Institut Mitag-Leffler programme Graphs, Hypergraphs, and Computing. Each problem contributor has…
These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discusses the $L$-functions attached to such sums, the "Weil…
This paper studies the complexity of classical modal logics and of their extension with fixed-point operators, using translations to transfer results across logics. In particular, we show several complexity results for multi-agent logics…
An idea of Hopf's for applying complex analysis to the study of constant mean curvature spheres is generalized to cover a wider class of spheres, namely, those satisfying a Weingarten relation of a certain type, namely H = f(H^2-K) for some…
The paper contains a survey of the results obtained during the last ten years in the theory of elliptic boundary problems in H\"ormander function spaces, developed by the authors, and other related results of modern analysis. The basics of…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
The research monograph gives the first systematic exposition of the elliptic (scalar and matrix) operators theory and elliptic boundary-value problems in the scales of Hilbert spaces of H\"ormander of the functions/distributions of…
This is an English translation of Reidemeister's book "Einf\"uhrung in die kombinatorische Topologie" from 1932, the first monograph on combinatorial group theory and topology, with some added comments by the translator and Warren Dicks.
The classical theory of elliptic curves with complex multiplication is a fundamental tool for studying the arithmetic of abelian extensions of imaginary quadratic fields. While no direct analogue is available for real quadratic fields, a…
A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…
We revisit the old work of de Paiva on the models of the Lambek Calculus in dialectica models making sure that the syntactic details that were sketchy on the first version got completed and verified. We extend the Lambek Calculus with a…
This paper develops explicit class field theory for orders: of rank 1 in any global function field -- Hayes theory -- and of rank 2 in real quadratic function fields -- Real Multiplication. The essential ingredient in the development of the…