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Showing 1 to 17 of 17 for “"Modular Form"”.
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Congruences for the Coefficients of Weakly Holomorphic Modular Forms
Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. In each case, the values of the given arithmetic function appear as the Fourier coefficients of a weakly holomorphic modular form. We show that similar …
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Representation by Quaternary Quadratic Forms whose Coefficients are 1, 2, 7 and 14
We determine explicit formulae for the number of representations of a positive integer n by the quaternary quadratic forms a_1x_1^2+a_2x_2^2+a_3x_3^2+a_4x_4^2, where a_1, a_2, a_3, a_4 in {1,2,7,14}. We use a modular form approach.
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The fundamental critical points of modular elliptic curves
… critical points of the normalized weight two modular form associated with an elliptic curve is an upper bound on the analytic rank of the curve. Their calculation of this quantity for all elliptic curves of conductor less than 424 confirmed that, with only 16 exceptions, the bound is sharp. It …
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p-adic Heights of Heegner points on Shimura curves
Let f be a primitive Hilbert modular form of weight 2 and level N for the totally real field F, and let p be an odd rational prime such that f is ordinary at all primes dividing p. When E is a CM extension of F of relative discriminant prime to Np, we give an explicit construction of the p-adic …
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OVERCONVERGENT MODULAR AND DE RHAM SHEAVES AND P-ADIC ITERATION OF THE GAUSS-MANIN CONNECTION
… sheaves of de Rham classes on Hilbert modular varieties in the case p is unramified in the totally real field. This is a generalization of the work of Andreatta-Iovita in the case of elliptic curves, using a technique that marks an improvement on their approach in terms of convergence …
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L-invariants and congruences for Galois representations of dimension 3, 4, and 8
… the two-dimensional representations attached to modular forms by Deligne. In particular, we shall study the Iwasawa theory of the adjoint representation, as well as certain double and triple products of Deligne's representations. In the first half we will undertake a computational study of …
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KMESS: an open source software package using a semi-empirical mesh-grid method for the modeling of germanium detector efficiencies
… of point sources. The code was written in a modular form, making it easy to adapt for other detector configurations and materials. A suite of webbased graphical front-end tools was also developed to make the execution of KMESS user-friendly. KMESS can predict most full-energy peak …
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Analogues of Dedekind Sums
… system of the Dedekind eta-function as a modular form. A century later, B. C. Berndt did analogous work with the classical theta-functions and introduced the sum$$S(d, c) = \sum\sbsp{j=1}{c-1}({-}1)\sp{j+1+\lbrack dj/c\rbrack},$$among others. There is considerable literature on the …
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Analytic and arithmetic applications of half integral weight automorphic forms
… arithmetic applications of half integral weight modular forms. In the first chapter we are motivated by a conjecture of Hoffstein (2011) that asserts that the L-series attached to a half integral weight modular form satisfies a Lindelof hypothesis. Using spectral and diophantine techniques, the …
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Some analytic aspects of Vafa-Witten twisted N̳ = 4 supersymmetric Yang-Millseory theory
… predicts that this partition function is a modular form. On the other hand, the Fourier coefficients of the partition function are supposed to be the "Euler characteristics" of various moduli spacesMASD of compactified anti-self-dual instantons. For several algebraic surfaces, these Euler …
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Software Simulation of an Unmanned Vehicle Performing Relative Spacecraft Orbits
… These two simulations are implemented in a modular form using the UMBRA framework. In addition, an interface between these two simulations is created for the unmanned vehicle to mimic the translational motion of a spacecraft's relative orbit. Finally, some of the limitations and future …
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Half-integral weight Kloosterman sums and integer partitions
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01
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Behavior of partition values modulo powers of primes
… arise naturally as theFourier coefficients of a modular form. Using the theory of modular forms, we study the behavior of <italic>p(n)</italic> and related partition statistics and relate partition values to other objects of interest in the theory of automorphic forms, the central critical values …
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An intelligent magnetic tape controller
… to control the tape drives. This is in the. form of an RSX-11 device driver written in PDP-11 assembler. To allow the particular to proposed local system allow area highly modular form. to be easily the system to network) , the upgraded in the future (in be incorporated into UCT's software …
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Computer-Aided Design and Simulation of Chemical Plants: PEETPACK, a Non-Proprietary Flowsheeting Program
… nature. PEETPACK is constructed in a highly modular form to facilitate its installation, further development and its ease of understanding by students and industrial users alike. It is composed of six sets of semi-independent programs: the data communicators, the calculation program, a …
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SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS
… of differential operators on sheaves of p-adic modular forms.