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

Riccardo Salvati-Manni, Jaap Top
1993 American Journal of Mathematics  
This Hg plays the same role in the theory 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')).  ... 
doi:10.2307/2374865 fatcat:gzyl7zt6ozckpirwwmefwbedni

Quantum variance on quaternion algebras, I [article]

Paul D. Nelson
2016 arXiv   pre-print
Our results compare 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.  ... 
arXiv:1601.02526v2 fatcat:jbs2faquibep5pkikq5tin7ooe

Manifestations of classical phase space structures in quantum mechanics

O. Bohigas, S. Tomsovic, D. Ullmo
1993 Physics reports  
Using two coupled quanic oscillators for illustration, the quantum mechanics 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).  ... 
doi:10.1016/0370-1573(93)90109-q fatcat:b7u66qgt3bgcjhwwngxboex5va

Smarandache Function Journal, 10 [article]

Sabin Tabirca, Tatiana Tabirca
1999 Zenodo  
SNJ is a referred journal: reviewed, indexed, cited, concerning any 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)  ... 
doi:10.5281/zenodo.8959 fatcat:brtc4c2aina5roy4kgg6nql6si

Factoring integers with the number field sieve [chapter]

J. P. Buhler, H. W. Lenstra, Carl Pomerance
1993 Lecture notes in mathematics  
The present paper is devoted 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  ... 
doi:10.1007/bfb0091539 fatcat:246frt7rh5hwfpc23vgtcf4ggq

Heegner points and derivatives ofL-series. II

B. Gross, W. Kohnen, D. Zagier
1987 Mathematische Annalen  
The authors would like 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  ... 
doi:10.1007/bf01458081 fatcat:35kxdnegd5ew5odk4e7hxq3ksq

Cycles on Siegel threefolds and derivatives of Eisenstein series

S Kudla
2000 Annales Scientifiques de l'Ecole Normale Supérieure  
is an ordinary 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  ... 
doi:10.1016/s0012-9593(00)01051-x fatcat:cluekqwzzzgdfbrqcbj2iwsium

Smarandache Function Journal, 14 [article]

Sabin Tabirca, Tatiana Tabirca
2003 Zenodo  
SNJ is a referred journal: reviewed, indexed, cited, concerning any 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.  ... 
doi:10.5281/zenodo.8973 fatcat:s3mrdjhufnfx7o5er4bwf6ukrm

On the topological structure of non-singular algebraic surfaces in CP3

R. Mandelbaum, B. Moishezon
1976 Topology  
and Q is CP* with orientation opposite 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).  ... 
doi:10.1016/0040-9383(76)90047-1 fatcat:nqjsfxaysveepoymvvw6otocl4

On the Precession of a Viscous Spheroid, and on the Remote History of the Earth

G. H. Darwin
1879 Philosophical Transactions of the Royal Society of London  
The fourteenth term 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.  ... 
doi:10.1098/rstl.1879.0073 fatcat:e5ke2szg7je45es74ppw255yfq

Fourier integral operators. I

Lars Hörmander
1971 Acta Mathematica  
Preface Pseudo-differential operators have been developed as a tool for the study 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.  ... 
doi:10.1007/bf02392052 fatcat:i2akqec7wzhwfplwtzsknrb6ei

Smarandache Function Journal, 13 [article]

Sabin Tabirca, Tatiana Tabirca
2002 Zenodo  
SNJ is a referred journal: reviewed, indexed, cited, concerning any 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.  ... 
doi:10.5281/zenodo.8968 fatcat:mjrkjhc25vdr5ova23qlszcua4

Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture [chapter]

J. S. Balakrishnan, A. J. Best, F. Bianchi, B. Lawrence, J. S. Müller, N. Triantafillou, J. Vonk
2021 PROGRESS IN MATHEMATICS  
The publisher, the authors, and the editors are safe 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  ... 
doi:10.1007/978-3-030-65203-6_2 fatcat:legvsgze6ffqzmgmvwg4irebvq

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

J. J. Sylvester
1864 Philosophical Transactions of the Royal Society of London  
The 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.  ... 
doi:10.1098/rstl.1864.0017 fatcat:bsmezi456fahdgh4rjb3fu3bx4

Four-dimensional topology: an introduction

Richard Mandelbaum
1980 Bulletin of the American Mathematical Society  
Now we can 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.  ... 
doi:10.1090/s0273-0979-1980-14687-x fatcat:7ntud2ptejcmffbrs67n7dcu5q
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