Related papers: Distinguishing eigenforms modulo a prime ideal

We study the average distribution of primes of size $x$ in arithmetic progressions to moduli larger than $x^{\frac{1}{2}}$. Using arithmetic information from the works of many authors together with different variants of the original…

In this article, we give some results on simultaneous non-vanishing and simultaneous sign-changes for the Fourier coefficients of two modular forms. More precisely, given two modular forms $f$ and $g$ with Fourier coefficients $a_n$ and…

We give an explicit dimension formula for paramodular forms of degree two of prime level with plus or minus sign of the Atkin--Lehner involution of weight $\det^k\operatorname{Sym}(j)$ with $k\geq 3$, as well as a dimension formula for…

If a module $M$ has finite projective dimension, then the Ext modules of $M$ against any other module eventually vanish and the projective dimension of $M$ gives a uniform bound for this vanishing. For modules of infinite projective…

Let $\mathcal{F}$ be a family of subsets of $[n]$ and $L$ be a subset of $[n]$. We say $\mathcal{F}$ is an $L$-differencing Sperner system if $|A\setminus B|\in L$ for any distinct $A,B\in\mathcal{F}$. Let $p$ be a prime and $q$ be a power…

Feigin and Shoikhet conjectured in math/0610410 that successive quotients $B_m(A_n)$ of the lower central series filtration of a free associative algebra $A_n$ have polynomial growth. In this paper we give a proof of this conjecture, using…

We give explicit upper bounds for the coefficients of arbitrary weight $k$, level 2 cusp forms, making Deligne's well-known $O(n^{\frac{k-1}{2}+\epsilon})$ bound precise. We also derive asymptotic formulas and explicit upper bounds for the…

In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound on the length of an $R_\eta$-sequence containing fixed $n$ forms of degree at most $d$ in polynomial rings over a field. This result…

Cannon, Floyd and Parry have studied the modulus of finite subdivision rules extensively. We investigate the properties of the modulus of subdivision rules with linear and exponential growth at every vertex, using barycentric subdivision…

Let $k$ and $n$ be positive even integers. For a Hecke eigenform $h$ in the Kohnen plus subspace of weight $k-n/2+1/2$ for $\varGamma_0(4)$, let $I_n(h)$ be the Duke-Imamoglu-Ikeda lift of $h$ to the space of cusp forms of weight $k$ for…

We find explicit bounds on the primary components and on the Castelnuovo-Mumford regularity of powers of monomial ideals. We also analyze the primary decompositions of Katzman's example.

Using the notion of higher-order Fourier dimension introduced in \cite{M2} (which was a sort of psuedorandomness condition stemming from the Gowers norms of Additive Combinatorics), we prove a maximal theorem and corresponding…

We investigate the numerical computation of Maass cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r=40000. These eigenvalues are the largest…

The main result of this paper is an instance of the conjecture made by Gouvea and Mazur (Math. Res. Lett., 1995) which asserts that for certain values of r the space of r-overconvergent p-adic modular forms of tame level N and weight k…

The paper deals with establishing bounds for Eisenstein series on congruence quotients of the upper half plane, with control of both the spectral parameter and the level. The key observation in this work is that we exploit better the…

Murthy and Sethi (Sankhya Ser B \textbf{27}, 201--210 (1965)) gave a sharp upper bound on the variance of a real random variable in terms of the range of values of that variable. We generalise this bound to the complex case and, more…

We examine canonical bases for weakly holomorphic modular forms of weight $0$ and level $p = 2, 3, 5, 7, 13$ with poles only at the cusp at $\infty$. We show that many of the Fourier coefficients for elements of these canonical bases are…

Let $p$ be a prime number. We study the slopes of $U_p$-eigenvalues on the subspace of modular forms that can be transferred to a definite quaternion algebra. We give a sharp lower bound of the corresponding Newton polygon. The computation…

Let $f$ be a newform of weight $2$ on $\Gamma_0(N)$ with Fourier $q$-expansion $f(q)=q+\sum_{n\geq 2} a_n q^n$, where $\Gamma_0(N)$ denotes the group of invertible matrices with integer coefficients, upper triangular mod $N$. Let $p$ be a…

The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the approach via the so-called inertia forms or…