Related papers: On Kudla's Green function for signature (2,2), par…

In this Ph.D. dissertation (2018, Emory University) we prove theorems at the intersection of the additive and multiplicative branches of number theory, bringing together ideas from partition theory, $q$-series, algebra, modular forms and…

Based on computeralgebra experiments we formulate a refined version of Green's conjecture and a conjecture of Schicho-Schreyer-Weimann which conjecturally also holds in positive characteristic. The experiments are done by using our…

The newly developed Gorkov-Green's function approach represents a promising path to the ab initio description of medium-mass open-shell nuclei. We discuss the implementation of the method at second order with a two-body interaction, with…

We define an integral version of Sczech's Eisenstein cocycle on GLn by smoothing at a prime ell. As a result we obtain a new proof of the integrality of the values at nonpositive integers of the smoothed partial zeta functions associated to…

We study Green functions for the pressure of stationary Stokes systems in a (possibly unbounded) domain $\Omega\subset \mathbb{R}^d$, where $d\ge 2$. We construct the Green function when coefficients are merely measurable in one direction…

Let $k$ be a finite field of characteristic $p$. In the 1960s, Kondo attached non-abelian Gauss sums to irreducible $\mathbb{C}$-representations of $\mathrm{GL}_n(k)$, and computed them in terms of Green parameters. On the other hand, the…

In this paper, we consider the relation between the simplest types of arithmetic theta series, those associated to the cycles on the moduli space $\Cal C$ of elliptic curves with CM by the ring of integers $\OK$ in an imaginary quadratic…

We define a cocycle on Gln using Shintani's method. It is closely related to cocycles defined earlier by Solomon and Hill, but differs in that the cocycle property is achieved through the introduction of an auxiliary perturbation vector Q.…

We determine the asymptotic behavior of the Arakelov metric, the Arakelov-Green's function, and the Faltings delta-invariant for arbitrary one-parameter families of complex curves with semistable degeneration. The leading terms in the…

The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for…

The rational cohomology of the moduli space of rank two, odd degree stable bundles over a curve (of genus g > 1) has been studied intensely in recent years and in particular the invariant subring generated by Newstead's generators alpha,…

In this note we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Also a few Beurling type hitting estimates are obtained for the random walk on discretizations of…

This is the first in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even…

We provide a new, elementary proof of the multiplicative independence of pairwise distinct $\mathrm{GL}_2^+(\mathbb{Q})$-translates of the modular $j$-function, a result due originally to Pila and Tsimerman. We are thereby able to…

In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…

We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conjecture for all GM varieties. We compute all integral Chow…

The special uniformity of zeta functions claims that pure non-abelian zeta functions coincide with group zeta functions associated to the special linear groups. Naturally associated are three aspects, namely, the analytic, arithmetic, and…

This survey grew out of notes accompanying a cycle of lectures at the workshop Modern Trends in Gromov-Witten Theory, in Hannover. The lectures are devoted to interactions between Hurwitz theory and Gromov-Witten theory, with a particular…

In 1951, Ankeny, Artin, and Chowla published a brief note containing four congruence relations involving the class number of $\mathbb{Q}(\sqrt{d})$ for positive squarefree integers $d\equiv 1 \bmod{4}$. Many of the ideas present in their…

The thermal Euclidean Green functions for Photons propagating in the Rindler wedge are computed employing an Euclidean approach within any covariant Feynman-like gauge. This is done by generalizing a formula which holds in the Minkowskian…