Related papers: Fermat's Last Theorem: Algebra and Number Theory
We prove an analogue of the prime number theorem for finite fields.
We introduce the notion of ends for algebras. The definition is analogous to the one in geometric group theory. We establish some relations to growth conditions and cyclic cohomology.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
We prove Roth type theorems in finite groups. Our main tool is the Triangle Removal Lemma of Ruzsa and Szemer\'edi.
A special theorem related to the Fagnano's problem is proved and an example of the theorem is shown in a golden rectangle.
This paper is submitted to Algebraic-Number-Theory Archives for validation by Number Theorists Community. It is an update of the previous versions ANT-0155, ANT-0170, ANT-0205, ANT-0237, ANT-0321, ANT-0333, and ANT-0356, of which the first…
Number of results in number theory have been developed using a new method. The Goldbach binary conjecture in strengthened formulation have been among them.
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
In this paper, we prove some new thickness theorems with partial derivatives. We give some applications. First, we give a simple criterion that can judge whether two scaled Cantor sets have non-empty intersection. Second, we prove under…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
Comments about the paper by Elsholz, Fermat's last theorem implies Euclid's infinitude of primes, (2021), and simplification.
This work contains two papers: the first published in 2022 and entitled "On the nature of some Euler's double equations equivalent to Fermat's last theorem" provides a marvellous proof through the so-called discordant forms of appropriate…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
This is a survey article on developments in modularity since the proof of Fermat's Last Theorem, with an emphasis on the historical development of the subject rather than any technical details.
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
In this essay, we see how prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime) can lead to elegant proofs of number theoretical concepts. We namely develop the notion…
We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing…
We give a convenient reformulation, a slight generalization and some applications of the formality transfer theorem for DG-Lie algebras.