Related papers: The fundamental theorem of complex multiplication

In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.

We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.

This note shows that the three theorems presented in J. Math. Anal. Appl. 556 (2026), 130199, whose proofs, in their present formulation, are purely formal, follow from elementary calculus.

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

This is an expository account of the proof of the theorem of Bourgain, Glibichuk and Konyagin which provides non-trivial bounds for exponential sums over very small multiplicative subgroups of prime finite fields.

A conference talk discussing the conjecture of Langlands and Rapoport concerning the structure of the points on a Shimura variety modulo a prime of good reduction.

Motivated by the study of a certain family of classical geometric problems we investigate the existence of multiplicative connections on proper Lie groupoids. We show that one can always deform a given connection which is only approximately…

A difference equation based method of determining two factors of a composite is presented. The feasibility of P-complexity is shown. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non…

We give here a general, best-possible, and smoothly-derived form of the Master Theorem for divide-and-conquer recurrences.

This is the second installment in a sequence of articles devoted to "explicit Chabauty-Kim theory" for the thrice punctured line. Its ultimate goal is to construct an algorithmic solution to the unit equation whose halting will be…

This paper contains a long summary of the basic properties of higher FR torsion. An attempt is made to simplify the constructions from my book Higher Franz-Reidemeister Torsion (IP/AMS Studies in Advanced Math 31). Some new basic theorems…

This is a collection of example computations that are cited in the Appendix of [DNT]. In each case, the aim is to show that the extension of a given finite simple group by an elementary abelian group of given rank has the property that not…

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

We present effective upper bounds on the symmetric bilinear complexity of multiplication in extensions of a base finite field Fp2 of prime square order, obtained by combining estimates on gaps between prime numbers together with an optimal…

Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.

This is an expository paper which explores the ideas of the authors' paper "From Affine Geometry to Complex Geometry", arXiv:0709.2290. We explain the basic ideas of the latter paper by going through a large number of concrete, increasingly…

We are looking for a formulation of Manin's real multiplication question in higher rank. This question comports, in our point of view, at least two steps: 1. a formalisation of the linear algebra side of the story in terms of morphisms of…

In this note we provide examples of families of Calabi-Yau 3-manifolds over Shimura varieties, whose mirror families contain subfamilies over Shimura varieties. Therefore these original families and subfamilies on the mirror side contain…

This is a revision of the paper that was previously entitled "Weighted Completion of Galois Groups and Some Conjectures of Deligne". Fix a prime number $\l$. We prove a conjecture stated by Ihara, which he attributes to Deligne, about the…

In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.