Related papers: On units generated by Euler systems
In this short paper we present an elementary proof of the infinitude of primes. Our proof is similar in spirit to Euler's proof that the reciprocals of primes diverges and only uses tools from elementary number theory and calculus. In…
We prove a "discrete analogue" for Taelman's class modules of certain Conjectures formulated by R. Greenberg for cyclotomic fields.
Linear harmonic number sums had been studied by a variety of authors during the last centuries, but only few results are known about nonlinear Euler sums of quadratic or even higher degree. The first systematic study on nonlinear Euler sums…
One familiar with the Euler zeta function, which established the remarkable relationship between the prime and composite numbers, might naturally ponder the results of the application of this special function in cases where there is no…
We explain how the unramified Plancherel formula in the relative Langlands program gives a natural way of constructing test vectors which satisfy the tame norm relations of an Euler system. This uniformly recovers many of the known Euler…
A solution to the part and whole problem is presented in this paper by using a complex mathematical representation that permits to define the Holon concept as a Basic Unit System that remains itself in spite of complex operations such as…
We prove a criterion that allows to construct units in product systems of correspondences with prescribed infinitesimal characterizations. This criterion summarizes proofs of known results and new applications. It also frees the hypothesis…
Let $\ell$ and $p$ be odd primes. For a positive integer $\mu$ let $k_\mu$ be the ray class field of $k=\mathbb{Q}(e^{2\pi i/\ell})$ modulo $2p^\mu$. We present certain class fields $K_\mu$ of $k$ such that $k_\mu\leq K_\mu\leq k_{\mu+1}$,…
The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field $K$. We derive bounds for this product in case $K$ is a prime cyclotomic field, distinguishing between whether there is a…
Let $E/\mathbb{Q}$ be an elliptic curve, let $p>2$ be a prime of good reduction for $E$, and assume that $E$ admits a rational $p$-isogeny with kernel $\mathbb{F}_p(\phi)$. In this paper we prove the cyclotomic Iwasawa main conjecture for…
We give a short proof, using generating functions, for a polynomial congruence for Eulerian polynomials first proved, using arrangements of hyperplanes, by Yoshinaga and later proved, using roots of unity, by Iijima, Sasaki, Takahashi, and…
We study the cohomology of an elliptic differential complex arising from the infinitesimal moduli of heterotic string theory. We compute these cohomology groups at the standard embedding, and show that they decompose into a direct sum of…
For a CM abelian extension $F/K$ of an arbitrary totally real number field $K$, we construct the Stickelberger splitting maps (in the sense of \cite{Ba1}) for both the \'etale and the Quillen $K$--theory of $F$ and we use these maps to…
We present results for infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-, two- and three-dimensional series. All these series can be expressed in terms of…
For a real abelian field and for an odd prime p splitting in the field, we study a map between the p-parts of the class group and of the quotient of units modulo Cyclotomic Units, respectively, along the cyclotomic Z_p-extension of the…
In this note, we describe a conjecture, that, for an odd prime p, relates special values of a cup product pairing on cyclotomic p-units in the pth cyclotomic field to the L-values of newforms satisfying modulo p congruences with Eisenstein…
This is an English translation of Euler's ``Theoremata circa residua ex divisione potestatum relicta'', Novi Commentarii academiae scientiarum Petropolitanae 7 (1761), 49-82. E262 in the Enestrom index. Euler gives many elementary results…
A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…
We prove a "twist-compatibility" result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology…
In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are associated to $p$-adic representations over number fields. We now…