Related papers: Multiple Dirichlet series associated to additive a…
We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce…
Friedberg, Hoffstein and Lieman have constructed two related multiple Dirichlet series from quadratic and higher-order $L$-functions and Gauss sums. We compute these multiple Dirichlet series explicitly in the case of the rational function…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of a discrete data determined by the images of parameters. In similar terms, we…
In the present paper, we establish an analytic continuation of Drinfeld logarithms by using the techniques introduced in [Fur20]. This result can be seen as an analogue of the analytic continuation of the elliptic integrals of the first…
Motivic characteristic classes of possibly singular algebraic varieties are homology class versions of motivic characteristics, not classes in the so-called motivic (co)homology. This paper is a survey on them with more emphasis on…
Whenever all differences between zeros of two holomorphic almost periodic functions in a strip form a discrete set, then both functions are infinite products of periodic functions with commensurable periods. In particular, the result is…
We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.
We study the additivity of various geometric invariants involved in Reimann-Roch type formulas and defined via the trace map. To do so in a general context we prove that given any Grothendieck category A, the derived category D(A) has a…
We prove that every Mahler series, over a field of characteristic $0$, with multiplicative coefficients is regular in the sense of Allouche and Shallit. We also obtain an explicit characterization of such series. This yields a joint…
We prove a characterization of the Dirichlet-Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.
Character language models have access to surface morphological patterns, but it is not clear whether or how they learn abstract morphological regularities. We instrument a character language model with several probes, finding that it can…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
For a positive irrational number $\alpha,$ we study the ordinary Dirichlet series $\zeta_\alpha(s) = \sum\limits_{n\geq1} \lfloor\alpha n\rfloor^{-s}$ and $S_\alpha(s) = \sum\limits_{n\geq1} (\left\lceil\alpha n\right\rceil - \left\lceil…
In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…
We derive a boundary monotonicity formula for a class of biharmonic maps with Dirichlet boundary conditions. A monotonicity formula is crucial in the theory of partial regularity in super-critical dimensions. As a consequence of such a…
We address some questions posed by Goss related to the modularity of Drinfeld modules of rank 1 defined over the field of rational functions in one variable with coefficients in a finite field. For each positive characteristic valued…
In the present paper, we introduce meromorphic Drinfeld modular forms of arbitrary rank equipped with a particular arithmeticity property. We also study their special values at CM points and show the algebraic independence of these values…