Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 10,000 papers for “Modular form”

Modular form and Cohomology

CHOIE, YOUNG JU · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2020

Cited by 0

Sums with modular form coefficients

M. N. Huxley · 1996

Abstract Remarks The second term in (20.1.7) appears when we pass from a smoothed sum in Lemma 10.3.1 (with N≍MT-1/3) to the sum (20.1.1). This term may be reduced by appealing to a stronger bound than Lemma 10.2.1, such as the full result of Rankin (1939) or the results of Moreno and Shahidi (1983) (Lemma 10.3.3) or Deligne (1974) (Lemma 10.3.2).

Cited by 0

Igusa's modular form and the classification of Siegel modular threefolds

Klaus Hulek · ArXiv.org · 1999

In this paper we prove two results concerning the classification of Siegel modular threefolds. Let A_{1,d}(n) be the moduli space of abelian surfaces with a (1,d)-polarization and a full level-n structure and let A_{1,d}^{lev}(n) be the space where one has fixed an additional canonical level structure. We prove that A_{1,d}(n) is of general type if (d,n)=1 and n ist at least 4. This is the best possible result which one can prove for all d simultaneously. Let p be an odd prime and assume that (p,n)=1. Then we prove that the Voronoi compactification of A_{1,p}^{lev}(n) is smooth and has ample canonical bundle if and only if n is greater than or equal to 5.

Cited by 0Open access

Drivers for free‐form modular displays

Pieter Bauwens, Jan Doutreloigne · Journal of the Society for Information Display · 2010

Abstract— When displays of different sizes and shapes are required, a modular display system seems to be a good solution. Many systems offer only a limited freedom of shapes. The display can be scaled, but no irregular shapes can be created. If those shapes can be created, the configuration is often manual. A more intelligent modular system allows all shapes to be created and configures automatically. This paper presents two drivers that can be used in such a modular system. The first driver ensures that the data finds its way to every module and is displayed, even if there are some “holes” in the display due to missing modules. The second driver adds some extra functionality. The precise display configuration can be detected, and in the graphical user interface (used for controlling the display) the user sees an updated view of the display configuration when modules are added or removed. Both drivers have been proven successful and results are presented in this paper.

Cited by 2

Exponential sums with modular form coefficients

M. N. Huxley · 1996

Abstract Modular forms, and their generalization to automorphic functions, lie at the centre of mathematics, in the sense that they appear in combinatorics, group theory, number theory, algebraic geometry, geometric topology, functional analysis, and complex analysis. Swinnerton-Dyer once declared that the unsolved problems in mathematics remain unsolved because we have not yet connected them to modular forms.

Cited by 0

THE MINIMAL MODULAR FORM ON QUATERNIONIC

Aaron Pollack · Journal of the Institute of Mathematics of Jussieu · 2020

Abstract Suppose that $G$ is a simple reductive group over $\mathbf{Q}$ , with an exceptional Dynkin type and with $G(\mathbf{R})$ quaternionic (in the sense of Gross–Wallach). In a previous paper, we gave an explicit form of the Fourier expansion of modular forms on $G$ along the unipotent radical of the Heisenberg parabolic. In this paper, we give the Fourier expansion of the minimal modular form $\unicode[STIX]{x1D703}_{Gan}$ on quaternionic $E_{8}$ and some applications. The $Sym^{8}(V_{2})$ -valued automorphic function $\unicode[STIX]{x1D703}_{Gan}$ is a weight 4, level one modular form on $E_{8}$ , which has been studied by Gan. The applications we give are the construction of special modular forms on quaternionic $E_{7},E_{6}$ and $G_{2}$ . We also discuss a family of degenerate Heisenberg Eisenstein series on the groups $G$ , which may be thought of as an analogue to the quaternionic exceptional groups of the holomorphic Siegel Eisenstein series on the groups $\operatorname{GSp}_{2n}$ .

Cited by 4

DS genes form a modular network.

Ilario De Toma (3251964), Cesar Sierra (11486010), Mara Dierssen (51655) · Figshare · 2021

<p>DS network where each node is a gene found DE in at least 4 comparisons. Edges represent co-DE events between genes colored based on the size of the co-DE cluster. Edge thickness is proportional to the number of occurrences of co-DE and the STRINGdb score. We did not plot the edges corresponding to co-DE pairs found in less than 4 comparisons). Size is proportional to the log<sub>2</sub> of the occurrences of DE. Genes encoded by HSA21 are depicted with a square, non-HSA21 with a circle. The significant enrichments for each module are indicated with boxes of different colors.</p>

Cited by 0Open access

MODULAR FORM CONGRUENCES AND SELMER GROUPS

William McGraw, Ken Ono · Journal of the London Mathematical Society · 2003

Motivated by Cremona and Mazur's notion of visibility of elements in Shafarevich–Tate groups [6, 27], there have been a number of recent works which test its compatibility with the Birch and Swinnerton–Dyer conjecture and the Bloch–Kato conjecture. These conjectures provide formulas for the orders of Shafarevich–Tate groups in terms of values of L-functions. For example, one may see recent work of Agashe, Dummigan, Stein and Watkins [1, 2, 10, 11]. In their examples, they find that the presence of visible elements agrees with the expected divisibility properties of the relevant L-values.

Cited by 10

Modular Advanced Composite Hull-Form (MACH) Technology

Vincent Caccese · 2002

Abstract : This progress report summarizes the first quarter of work on the Modular Advanced Composite Hullform (MACH) project. The primary tasks covered in this quarter are: (1) development of concepts and criteria for hybrid structures and connections; (2) develop criteria for structural monitoring system; and (3) further the design of the underwater body for the HYSWAC. Review of a connection evaluation are summarized along with identification of issues related to implementation of hybrid connections in underwater environments.

Cited by 0

Lambert series associated to Hilbert modular form

Rishabh Agnihotri · International Journal of Number Theory · 2021

In 1981, Zagier conjectured that the Lambert series associated to the weight 12 cusp form [Formula: see text] should have an asymptotic expansion in terms of the nontrivial zeros of the Riemann zeta function. This conjecture was proven by Hafner and Stopple. In 2017 and 2019, Chakraborty et al. established an asymptotic relation between Lambert series associated to any primitive cusp form (for full modular group, congruence subgroup and in Maass form case) and the nontrivial zeros of the Riemann zeta function. In this paper, we study Lambert series associated with primitive Hilbert modular form and establish similar kind of asymptotic expansion.

Cited by 5

From pseudodifferential analysis to modular form theory

André Unterberger · Journées Équations aux dérivées partielles · 1999

Taking advantage of methods originating with quantization theory, we try to get some better hold - if not an actual construction - of Maass (non-holomorphic) cusp-forms. We work backwards, from the rather simple results to the mostly devious road used to prove them.

Cited by 0Open access

Modular Short Form Videos for Library Instruction

Cindy Craig · SHILAP Revista de lepidopterología · 2017

In Brief Expensive software isn’t necessary to create effective tutorials. Quick, unedited tutorials created on social media, such as on Instagram or Snapchat, may be more effective. These short form videos (SFVs) combine the advantages of animated GIFs with the advantages of screencasts: modularity, repetition of steps, and animated visuals supported by pertinent audio. SFVs are cheap (or free) and easy to make with materials libraries already possess, such as Internet access, computers, and smartphones. They are easily replaceable if the subject changes. The short form forces librarians to get right to the point. Finally, SFVs are easily disseminated on social media and have the potential to go viral.

Cited by 0Open access

The Mandelbrot Set as a Modular Form

Linas Vepstas · 2005

An exploration of the interior or the Mandelbrot Set and the appearance of functions appearing to be similar to modular forms. This provides yet another ex-ample of the close interconnection between the structure of the Modular Group SL(2,Z) and fractals. The relationship is demonstrated computationally and visu-ally, and not from first principles; visually, the interior resembles the Weierstrass elliptic invariant g2. However, it is a resemblance only; the various explicit ex-pressions that can be found are shown to not actually be modular forms. It is hypothesized that some simple but currently unknown transformation will convert them into modular forms. The construction of the interior is based on averaging together iterated values with a spectral-type summation, and then analyzing the asymptotic behavior of the sum. Leading divergence are easy to explain and remove; the remaining finite parts hint at modular symmetry. This is a work in progress. A final conclusion and analysis has not been reached. This paper is part of a set of chapters that explore the relationship between the real numbers, the modular group, and fractals. Updated and revised versions of this monograph can be found at

Cited by 0