Related papers: On a problem \`a la Kummer-Vandiver for function f…
We introduce some generalizations of the Euler-Kronecker constant of a number field and study their arithmetic nature.
We study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums of arbitrary two elements in the subset of quadratic surfaces…
We build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other…
We analyse the diagonal quotient for products of certain Artin--Schreier curves. The smooth models are almost always surfaces of general type, with Chern slopes tending asymptotically to 1. The calculation of numerical invariants relies on…
The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood from the multiplication in the space of…
We prove some novel multi-parameter point-line incidence estimates in vector spaces over finite fields. While these could be seen as special cases of higher-dimensional incidence results, they outperform their more general counterparts in…
We study the shifted convolution sum of the divisor function and some other arithmetic functions.
We present a reduction of the function field Mordell-Lang conjecture to the function field Manin-Mumford conjecture, in all characteristics, via model theory, but avoiding recourse to the dichotomy theorems for (generalized) Zariski…
We recast into histories-based form a quantum field theory defined earlier in operator language for a free scalar field on a background causal set. The resulting decoherence-functional resembles that of the continuum theory. The counterpart…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra…
Let F be a nonarchimedean local field and let G = GL(n) = GL(n,F). Let E/F be a finite Galois extension. We investigate base change E/F at two levels: at the level of algebraic varieties, and at the level of K-theory. We put special…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
In this note, we establish a Vorono\"i--Oppenheim summation formula for divisor functions over an arbitrary number field.
The Grothendieck and Artin-Mumford exact sequences for the Brauer group of a function field in 1 or 2 variables are applied to derive reciprocity laws for $q$th power residues.
We present a new variant of the quantum adversary method. All adversary methods give lower bounds on the quantum query complexity of a function by bounding the change of a progress function caused by one query. All previous variants…
This paper provides applications of patching to quadratic forms and central simple algebras over function fields of curves over henselian valued fields. In particular, we use a patching approach to reprove and generalize a recent result of…
We prove the generic base change theorem for stacks, and give an exposition on the lisse-analytic topos of complex analytic stacks, proving some comparison theorems between various derived categories of complex analytic stacks. This enables…
We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…
In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one…