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Cusp Forms of Weight 2 for the Group Γ 2 (4, 8)

1993
*
American Journal of Mathematics
*

This Hg plays the same role in the theory

doi:10.2307/2374865
fatcat:gzyl7zt6ozckpirwwmefwbedni
*of*abelian varieties over the complex*numbers*, as the usual upper half plane does in the theory*of**elliptic**curves*. ... Using this lifting procedure he is able*to*prove his conjecture for simple abelian surfaces which are (upto isogeny) factors*of*the jacobian*of*a modular*curve*Xo(p) where p is a prime*number*not*congruent*... For any pair*of*odd theta characteristics m = (ml,*m2*,M3,M4) and n = (*nl*,*n2*, n3, 2trace(tMx) det(X +M) exp ri(trace((X +M')T(X +M')). ...##
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Quantum variance on quaternion algebras, I
[article]

2016
*
arXiv
*
pre-print

Our results compare

arXiv:1601.02526v2
fatcat:jbs2faquibep5pkikq5tin7ooe
*to*those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular*curve*, whose method required a cusp. ... Our method uses the theta correspondence*to*reduce the problem*to*the estimation*of*metaplectic Rankin--Selberg convolutions. We apply it here*to*the first non-split case. ... We are grateful*to*many people for their contributions*to*this project. P. Sarnak introduced us*to*his work with W. ...##
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Manifestations of classical phase space structures in quantum mechanics

1993
*
Physics reports
*

Using two coupled quanic oscillators for illustration, the quantum mechanics

doi:10.1016/0370-1573(93)90109-q
fatcat:b7u66qgt3bgcjhwwngxboex5va
*of*simple systems whose classical analogs have varying degrees*of*non-*integrability*is investigated. ... This allows us*to*probe deeply into the workings*of*semiclassical quantizatlon in mixed phase space systems. Some observations*of*intermediate status states are made. ... One*of*us (S.T.) was supported by the Joliot-Curie Foundation, the Centre National de la Recherche Scientifique and the National Science Foundation (Grant*number*CHE-90l4555). ...##
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Smarandache Function Journal, 10
[article]

1999
*
Zenodo
*

SNJ is a referred journal: reviewed, indexed, cited, concerning any

doi:10.5281/zenodo.8959
fatcat:brtc4c2aina5roy4kgg6nql6si
*of*Smarandache type functions,*numbers*, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, etc. ... Acknowledgements We wish*to*express our gratitude*to*Professor Adelina Georgescu for her important contribution*to*the English translation*of*this paper. ... (*nl*~*n2*)), we have a dd(do ) = a d{ sdAnJ'iSdd(*nl*~*n2*)) = = a dASdAnl))'ia dd( Sdd(*nl*~*n2*) )~*nl*'i*nl*=*nl*· Thus, we obtain the contradiction Sdd(*nl*)~do <SdAn l )· So, if the sequence add is a (sds) ...##
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Factoring integers with the number field sieve
[chapter]

1993
*
Lecture notes in mathematics
*

The present paper is devoted

doi:10.1007/bfb0091539
fatcat:246frt7rh5hwfpc23vgtcf4ggq
*to*the description and analysis*of*a more general version*of*the*number*field sieve. ... This is asymptotically faster than all other known factoring algorithms, such äs the quadratic sieve and the*elliptic**curve*method. ... For mi one tries several values with m^ κ,*nl*^d+l\ until one discovers a value for which n -mf is found*to*have a divisor m^ with mi « n1/^"1"1^; for example, by trial division or by the*elliptic**curve*...##
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Heegner points and derivatives ofL-series. II

1987
*
Mathematische Annalen
*

The authors would like

doi:10.1007/bf01458081
fatcat:35kxdnegd5ew5odk4e7hxq3ksq
*to*thank the Max-Planck-lnstitut fiir Mathematik (Bonn, Germany) and the Mathematical Sciences Research Institute (Berkeley, USA), who made it possible for them*to*collaborate on ... We let n denote the Tate parameter q on the family*of*degenerating*elliptic**curves*near or*. ... First*of*all, there clearly is a decomposition N = N 1*N2*with (N1,*N2*) = (N1,*m2*) =(*N2*, ml)= 1: we write N as a product*of*prime powers ff and include p~ into N~ ifplm ~ and into either N 1 or N 2 ifp ...##
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Cycles on Siegel threefolds and derivatives of Eisenstein series

2000
*
Annales Scientifiques de l'Ecole Normale Supérieure
*

is an ordinary

doi:10.1016/s0012-9593(00)01051-x
fatcat:cluekqwzzzgdfbrqcbj2iwsium
*elliptic**curve*. ...*related**to*the value*of*the height pairing*of*a pair*of*arithmetic cycles on a Shimura*curve*. ... ->• a; 771 be an involution*of*C\ whose restriction*to*F is trivial. Suppose that there is a (unitary) homomorphism^: Ci=*M2*(B^)^E=Ms (B) such that ...##
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Smarandache Function Journal, 14
[article]

2003
*
Zenodo
*

SNJ is a referred journal: reviewed, indexed, cited, concerning any

doi:10.5281/zenodo.8973
fatcat:s3mrdjhufnfx7o5er4bwf6ukrm
*of*Smarandache type functions,*numbers*, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, etc. ... In particular, if a projection*of*an s-line has a slope that is a rational multiple*of*-.)3, then it will intersect edges and vertices in only a limited*number**of*ways. ... The arguments presented here hold in any s-manifold, except for the parts depending on there being a [mite,*number**of*triangles. ...##
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On the topological structure of non-singular algebraic surfaces in CP3

1976
*
Topology
*

and Q is CP* with orientation opposite

doi:10.1016/0040-9383(76)90047-1
fatcat:nqjsfxaysveepoymvvw6otocl4
*to*the usual. ... THE topological structure*of*non-singular algebraic surfaces in CP3 is discussed. ... image*of*the non-singular*elliptic**curve*C which is blown up at 9 points by v-processes). ...##
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On the Precession of a Viscous Spheroid, and on the Remote History of the Earth

1879
*
Philosophical Transactions of the Royal Society of London
*

The fourteenth term

doi:10.1098/rstl.1879.0073
fatcat:e5ke2szg7je45es74ppw255yfq
*of*V can raise no proper tide, because it is independent*of*the time, but it produces a permanent increment*to*the*ellipticity**of*the mean spheroid. ... values; moreover, the differential equn,tions*to*be*integrated*were so complex, that a laborious treatment, partly by analysis and partly by numei·ical quadratures, was the only method that I was able ... i i right-hand side from f*to*1; and this is equal*to*log tan 2 2 -log tan 2 f The*integration*was divided into a*number**of*periods, just as in the*solution**of*Section 15. ...##
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Fourier integral operators. I

1971
*
Acta Mathematica
*

Preface Pseudo-differential operators have been developed as a tool for the study

doi:10.1007/bf02392052
fatcat:i2akqec7wzhwfplwtzsknrb6ei
*of**elliptic*differential equations. ... Pseudo-differential operators as well as our Fourier*integral*operators are intended*to*make it possible*to*handle differential operators with variable coefficients roughly as one would handle differential ... There is another way*of*defining a section*of*~_~(T,~(M)/Tm(*M2*)) over M which is better*related**to*our definitions in sections 2.4 and 3.2. ...##
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Smarandache Function Journal, 13
[article]

2002
*
Zenodo
*

SNJ is a referred journal: reviewed, indexed, cited, concerning any

doi:10.5281/zenodo.8968
fatcat:mjrkjhc25vdr5ova23qlszcua4
*of*Smarandache type functions,*numbers*, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, etc. ... Acknowledgements Thanks*to*the Yahoo Smarandache Geometry Club for the interesting discussions and ideas that lead*to*this paper. ... Thus, (4.6) has no*solutions*(n, k). The theorem is proved. Theorem For any positive integer n, the inequality (1) holds. Proof We may assume thatPn> 10 7 • Then we have n> 1000. ...##
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Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture
[chapter]

2021
*
PROGRESS IN MATHEMATICS
*

The publisher, the authors, and the editors are safe

doi:10.1007/978-3-030-65203-6_2
fatcat:legvsgze6ffqzmgmvwg4irebvq
*to*assume that the advice and information in this book are believed*to*be true and accurate at the date*of*publication. ... The use*of*general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence*of*a specific statement, that such names are exempt from ... We thank Levent Alpoge, Netan Dogra, Kiran Kedlaya, Minhyong Kim, Bjorn Poonen, Michael Stoll, Akshay Venkatesh, and John Voight for many useful conversations and suggestions*relating**to*the material in ...##
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Algebraical Researches, Containing a Disquisition on Newton's Rule for the Discovery of Imaginary Roots, and an Allied Rule Applicable to a Particular Class of Equations, Together with a Complete Invariantive Determination of the Character of the Roots of the General Equation of the Fifth Degree, c

1864
*
Philosophical Transactions of the Royal Society of London
*

The

doi:10.1098/rstl.1864.0017
fatcat:bsmezi456fahdgh4rjb3fu3bx4
*solution*offered by M. ... Thus the following theorem may be demonstrated without diffi culty, viz., in any conjugate equation the*number**of*coupled roots is*congruent**to*0 in respect*to*the modulus 4 when the discriminant is positive ... and the 0 or 8 from that*of*4, and, finally, 0 and 8 from each other-the reduction*of*cases apparently depending upon the*relation**of*the index*of*the equation*to*the powers*of*the*number*2. ...##
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Four-dimensional topology: an introduction

1980
*
Bulletin of the American Mathematical Society
*

Now we can

doi:10.1090/s0273-0979-1980-14687-x
fatcat:7ntud2ptejcmffbrs67n7dcu5q
*relate*0 (*>, ƒ)*to*the Pontryagin*numbers**of*M and we find that p x (M) = ±20 (*%ƒ). Thus p x (M) = 0 (mod 48). ... are*congruent*. ...
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