In 1988, Gross proposed a conjectural congruence between Stickelberger elements and algebraic regulators, which is often referred to as the refined class number formula. this paper, we prove congruence.

Nous étudions une quantité KVol liée au volume sur la strate ℋ(2) des surfaces de translation genre 2, avec singularité conique. donnons suite explicite L(n,n) telles que KVol(L(n,n))→2 quand n tend vers l’infini, 2 étant l’infimum conjectural ℋ(2).

We study a conjectural formula for the maximal elements in wavefront set associated with theta representation of covering group over p-adic fields. In particular, it is shown that agrees existing work literature various families groups. also recapitulate results an analogous archimedean case, which motivated setting.

This proposal falls broadly in the area of number theory and more specifically in arithmetic geometry. It is concerned with a part of the Birch and Swinnerton-Dyer (BSD) conjecture on elliptic curves and abelian varieties. A fundamental problem of number theory is: given a set of polynomial equations with rational coefficients, find all of its rational solutions and investigate their structure....

The analogy between algebraic K-theory and cyclic homology is used to build a program aiming at understanding the algebraic K-theory of fields and the periodicity phenomena in algebraic K-theory. In particular, we conjecture the existence of a Leibniz K-theory which would play the role of Hochschild homology. We propose a motivated presentation for the Leibniz K2-group of a field. Mathematics S...

Adopting an evolutionary approach, we explain the conjectural variations firms may hold in duopoly. Given conjectures, firms play the market game rationally. Success in the market game determines fitness in the evolutionary game. Based on linear heterogeneous Cournot and Bertrand competition models, we show that the unique conjectures that are evolutionarily stable are consistent in that they a...

We state conjectures on the relationships between automorphic representations and Galois representations, and give evidence for them.

Recently it has been shown that consistent conjectures are evolutionarily stable. In this note we show that this finding depends on the use of the infinite population ESS (Maynard-Smith, Evolution and the theory of games, Cambridge University Press, Cambridge, UK, 1982). When applying the finitepopulation ESS (Schaffer, J Theor Biol 132:469–478, 1988) we show that the conjectures surviving in t...