Zobrazeno 1 - 10
of 278
pro vyhledávání: '"Duda, David"'
We prove the existence of murmurations in the family of Maass forms of weight 0 and level 1 with their Laplace eigenvalue parameter going to infinity (i.e., correlations between the parity and Hecke eigenvalues at primes growing in proportion to the
Externí odkaz:
http://arxiv.org/abs/2409.00765
Autor:
Bourdon, Abbey, Hashimoto, Sachi, Keller, Timo, Klagsbrun, Zev, Lowry-Duda, David, Morrison, Travis, Najman, Filip, Shukla, Himanshu
We develop an algorithm to test whether a non-CM elliptic curve $E/\mathbb{Q}$ gives rise to an isolated point of any degree on any modular curve of the form $X_1(N)$. This builds on prior work of Zywina which gives a method for computing the image o
Externí odkaz:
http://arxiv.org/abs/2311.07740
For a fixed natural number $h$, we prove meromorphic continuation of the two-variable Dirichlet series $\sum_m r_2(m) \sigma_w(m + h) (m + h)^{-s + w}$ to $\mathbb{C}^2$ and use this to obtain asymptotics for $\sum_{m^2 + n^2 \leq X} \sigma_w(m^2 + n
Externí odkaz:
http://arxiv.org/abs/2310.13632
We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor
Externí odkaz:
http://arxiv.org/abs/2310.07746
Let $f(z) = \sum A(n) n^{(k-1)/2} e(nz)$ be a cusp form of weight $k \geq 3$ on $\Gamma_0(N)$ with character $\chi$. By studying a certain shifted convolution sum, we prove that $\sum_{n \leq X} A(n^2+h) = c_{f,h} X + O_{f,h,\epsilon}(X^{\frac{3}{4}+
Externí odkaz:
http://arxiv.org/abs/2301.11901
Autor:
Anderson, Theresa C., Gafni, Ayla, Hughes, Kevin, Oliver, Robert J. Lemke, Lowry-Duda, David, Thorne, Frank, Wang, Jiuya, Zhang, Ruixiang
We study the number of degree $n$ number fields with discriminant bounded by $X$. In this article, we improve an upper bound due to Schmidt on the number of such fields that was previously the best known upper bound for $6 \leq n \leq 94$.
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Externí odkaz:
http://arxiv.org/abs/2204.01651
We study the properties of certain graphs involving the sums of primes. Their structure largely turns out to relate to the distribution of prime gaps and can be roughly seen in Cram\'er's model as well. We also discuss generalizations to the Gaussian
Externí odkaz:
http://arxiv.org/abs/2111.02795
Autor:
Lowry-Duda, David
We study sign changes in the sequence $\{ A(n) : n = c^2 + d^2 \}$, where $A(n)$ are the coefficients of a holomorphic cuspidal Hecke eigenform. After proving a variant of an axiomatization for detecting and quantifying sign changes introduced by Meh
Externí odkaz:
http://arxiv.org/abs/2108.12520
Autor:
Anderson, Theresa C., Gafni, Ayla, Oliver, Robert J. Lemke, Lowry-Duda, David, Shakan, George, Zhang, Ruixiang
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert's Irreducibility Theorem for degree $n$ polynomials $f$ with $\mathrm
Externí odkaz:
http://arxiv.org/abs/2107.02914
Autor:
Lowry-Duda, David, Sakareassen, Adam
Modular forms are highly self-symmetric functions studied in number theory, with connections to several areas of mathematics. But they are rarely visualized. We discuss ongoing work to compute and visualize modular forms as 3D surfaces and to use the
Externí odkaz:
http://arxiv.org/abs/2104.15116