Anastassiades, Christos

To each regular algebraic, conjugate self-dual, cuspidal automorphic representation $\Pi$ of $\mathrm{GL}(N)$ over a CM number field $E$ (or, more generally, to a regular algebraic isobaric sum of conjugate self-dual, cuspidal representations), we can attach a continuous $\ell$-adic Galois representation $r(\Pi)$ of the absolute Galois group of $E$...

Carney, Alexander

In one of the fundamental results of Arakelov’s arithmetic intersection theory, Faltings and Hriljac (independently) proved the Hodge-index theorem for arithmetic surfaces by relating the intersection pairing to the negative of the Neron-Tate height pairing. More recently, Moriwaki and Yuan–Zhang generalized this to higher dimension. In this work, ...

Nguyen, Jennifer

Let F_q be a finite field and let D ⊆ F_q. Let m be a positive integer and let k be an integer such that 1 ≤ k ≤ |D|. For b = (b_1,...,b_m) ∈ (F_q)^m , let N_m(k,b) denote the number of subsets S ⊆ D with cardinality k such that for i = 1,...,m, the sum, over a ∈ S, of a^i = b_i. The Moments Subset Sum Problem is to determine if N_m(k,b) > 0. There...

McAdam, Taylor Jane

We study the asymptotic distribution of almost-prime entries in horospherical flows on the quotient of SL(n,R) by a lattice, where the lattice is either cocompact or SL(n,Z). In the cocompact case, we obtain a result that implies density for almost-primes in horospherical flows where the number of prime factors is independent of the basepoint, and ...

Riffaut, Antonin

À partir du théorème d’André en 1998, qui est la première contribution non triviale à la conjecture de André-Oort sur les sous-variétés spéciales des variétés de Shimura, la principale problématique de cette thèse est d’étudier les propriétés diophantiennes des modules singuliers, en caractérisant les points de multiplication complexe (x; y) satisf...

Petro, Kolosov

In this paper described numerical expansion of natural-valued power function $x^n$, in point $x=x_0$ where $(n, \ x_0)$ - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared with solutions according to Newton’s Binomial theorem an...

Kolosov, Petro

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{\mathrm{A287326}}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{\mathrm{A287326}}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...

Petro, Kolosov

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence $\href{https://oeis.org/A287326}{A287326}$ in OEIS. The main property of $\href{https://oeis.org/A287326}{A287326}$ that it returns a perfect cube $n$ as sum of $n$-th row terms over $k, \ 0\leq k\leq n-1$ or $1\leq k\leq n$, by means of its symm...