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Journal articles on the topic 'Saito–Kurokawa lifts'

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Published: 6 September 2023

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1

Ichino, Atsushi. "Pullbacks of Saito-Kurokawa lifts." Inventiones mathematicae 162, no. 3 (July 18, 2005): 551–647. http://dx.doi.org/10.1007/s00222-005-0454-z.

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2

BROWN, JIM, and AMEYA PITALE. "Special values of L-functions for Saito–Kurokawa lifts." Mathematical Proceedings of the Cambridge Philosophical Society 155, no. 2 (May 2, 2013): 237–55. http://dx.doi.org/10.1017/s0305004113000224.

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AbstractIn this paper we obtain special value results for L-functions associated to classical and paramodular Saito–Kurokawa lifts. In particular, we consider standard L-functions associated to Saito–Kurokawa lifts as well as degree eight L-functions obtained by twisting with an automorphic form defined on GL(2). The results are obtained by combining classical and representation theoretic arguments.
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3

Mizuno, Yoshinori, and Shoyu Nagaoka. "Some congruences for Saito-Kurokawa lifts." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 80, no. 1 (October 21, 2009): 9–23. http://dx.doi.org/10.1007/s12188-009-0029-9.

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4

BROWN, JIM. "SPECIAL VALUES OF L-FUNCTIONS ON GSp4 × GL2 AND THE NON-VANISHING OF SELMER GROUPS." International Journal of Number Theory 06, no. 08 (December 2010): 1901–26. http://dx.doi.org/10.1142/s1793042110003769.

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In this paper, we show how one can use an inner product formula of Heim giving the inner product of the pullback of an Eisenstein series from Sp10 to Sp 2 × Sp 4 × Sp 4 with a new-form on GL2 and a Saito–Kurokawa lift to produce congruences between Saito–Kurokawa lifts and non-CAP forms. This congruence is in part controlled by the L-function on GSp 4 × GL 2. The congruence is then used to produce nontrivial torsion elements in an appropriate Selmer group, providing evidence for the Bloch–Kato conjecture.
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5

Das, Soumya, and Jyoti Sengupta. "An Omega-result for Saito-Kurokawa lifts." Proceedings of the American Mathematical Society 142, no. 3 (November 19, 2013): 761–64. http://dx.doi.org/10.1090/s0002-9939-2013-11797-1.

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6

Agarwal, Mahesh, and Jim Brown. "Saito–Kurokawa lifts of square-free level." Kyoto Journal of Mathematics 55, no. 3 (September 2015): 641–62. http://dx.doi.org/10.1215/21562261-3089127.

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7

Chen, Shih-Yu. "Pullback formulae for nearly holomorphic Saito–Kurokawa lifts." manuscripta mathematica 161, no. 3-4 (February 12, 2019): 501–61. http://dx.doi.org/10.1007/s00229-019-01111-2.

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8

Brown, Jim. "An inner product relation on Saito-Kurokawa lifts." Ramanujan Journal 14, no. 1 (September 21, 2006): 89–105. http://dx.doi.org/10.1007/s11139-006-9005-5.

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9

Xue, Hang. "Fourier–Jacobi periods of classical Saito–Kurokawa lifts." Ramanujan Journal 45, no. 1 (October 7, 2016): 111–39. http://dx.doi.org/10.1007/s11139-016-9829-6.

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10

Brown, Jim. "Saito–Kurokawa lifts and applications to the Bloch–Kato conjecture." Compositio Mathematica 143, no. 02 (March 2007): 290–322. http://dx.doi.org/10.1112/s0010437x06002466.

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11

DUMMIGAN, NEIL. "CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES." Glasgow Mathematical Journal 64, no. 2 (October 14, 2021): 504–25. http://dx.doi.org/10.1017/s0017089521000331.

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AbstractFollowing Ryan and Tornaría, we prove that moduli of congruences of Hecke eigenvalues, between Saito–Kurokawa lifts and non-lifts (certain Siegel modular forms of genus 2), occur (squared) in denominators of central spinor L-values (divided by twists) for the non-lifts. This is conditional on Böcherer’s conjecture and its analogues and is viewed in the context of recent work of Furusawa, Morimoto and others. It requires a congruence of Fourier coefficients, which follows from a uniqueness assumption or can be proved in examples. We explain these factors in denominators via a close examination of the Bloch–Kato conjecture.
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12

DUMMIGAN, NEIL. "CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES." Glasgow Mathematical Journal 64, no. 2 (October 14, 2021): 504–25. http://dx.doi.org/10.1017/s0017089521000331.

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AbstractFollowing Ryan and Tornaría, we prove that moduli of congruences of Hecke eigenvalues, between Saito–Kurokawa lifts and non-lifts (certain Siegel modular forms of genus 2), occur (squared) in denominators of central spinor L-values (divided by twists) for the non-lifts. This is conditional on Böcherer’s conjecture and its analogues and is viewed in the context of recent work of Furusawa, Morimoto and others. It requires a congruence of Fourier coefficients, which follows from a uniqueness assumption or can be proved in examples. We explain these factors in denominators via a close examination of the Bloch–Kato conjecture.
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13

Anamby, Pramath, and Soumya Das. "Bounds for the Petersson norms of the pullbacks of Saito–Kurokawa lifts." Journal of Number Theory 191 (October 2018): 289–304. http://dx.doi.org/10.1016/j.jnt.2018.03.011.

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14

Liu, Sheng-Chi, and Matthew P. Young. "Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts." American Journal of Mathematics 136, no. 1 (2014): 165–201. http://dx.doi.org/10.1353/ajm.2014.0008.

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15

Brown, Jim. "On the congruences primes of Saito-Kurokawa lifts of odd square-free level." Mathematical Research Letters 17, no. 5 (2010): 977–91. http://dx.doi.org/10.4310/mrl.2010.v17.n5.a14.

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16

Pal, Aprameyo, and Carlos de Vera-Piquero. "Pullbacks of Saito-Kurokawa Lifts and a Central Value Formula for Degree 6 $L$-Series." Documenta Mathematica 24 (2019): 1935–2036. http://dx.doi.org/10.4171/dm/719.

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17

Matthes, Roland. "The Saito–Kurokawa lift and Siegel’s theta series." International Journal of Number Theory 13, no. 07 (February 2017): 1679–93. http://dx.doi.org/10.1142/s1793042117500968.

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The aim of this paper is to give another short proof of the Saito–Kurokawa lift based on a converse theorem of Imai as was already done by Duke and Imamoglu. In contrast to their proof we avoid spectral analysis but use a real analytic Eisenstein series in a suitable Rankin–Selberg integral involving Siegel’s theta series.
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18

RYAN, NATHAN C., and GONZALO TORNARÍA. "A BÖCHERER-TYPE CONJECTURE FOR PARAMODULAR FORMS." International Journal of Number Theory 07, no. 05 (August 2011): 1395–411. http://dx.doi.org/10.1142/s1793042111004629.

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In the 1980s Böcherer formulated a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a Siegel modular form F to the coefficients of F. He proved the conjecture when F is a Saito–Kurokawa lift. Later Kohnen and Kuß gave numerical evidence for the conjecture in the case when F is a rational eigenform that is not a Saito–Kurokawa lift. In this paper we develop a conjecture relating the central value of the quadratic twists of the spinor L-function attached to a paramodular form and the coefficients of the form. We prove the conjecture in the case when the form is a Gritsenko lift and provide numerical evidence when it is not a lift.
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19

Pollack, Aaron. "A quaternionic Saito–Kurokawa lift and cusp forms on G2." Algebra & Number Theory 15, no. 5 (June 30, 2021): 1213–44. http://dx.doi.org/10.2140/ant.2021.15.1213.

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20

Matthes, Roland. "A NOTE ON THE SAITO-KUROKAWA LIFT FOR HERMITIAN FORMS." JP Journal of Algebra, Number Theory and Applications 40, no. 4 (August 31, 2018): 407–27. http://dx.doi.org/10.17654/nt040040407.

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21

Okazaki, Takeo, and Takuya Yamauchi. "A Siegel modular threefold and Saito-Kurokawa type lift to S 3(Γ1,3(2))." Mathematische Annalen 341, no. 3 (January 8, 2008): 589–601. http://dx.doi.org/10.1007/s00208-007-0204-1.

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22

Adersh, V. K., M. Manickam, and M. M. Sreejith. "On newforms and Saito-Kurokawa lifts." Journal of Number Theory, February 2023. http://dx.doi.org/10.1016/j.jnt.2023.01.005.

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23

Marzec, Jolanta. "Maass relations for Saito–Kurokawa lifts of higher levels." Ramanujan Journal, July 22, 2020. http://dx.doi.org/10.1007/s11139-020-00250-5.

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24

Kumari, Moni. "Comparing Hecke eigenvalues of Siegel eigenforms." Forum Mathematicum, December 17, 2022. http://dx.doi.org/10.1515/forum-2021-0319.

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Abstract This article deals with various kinds of quantitative results about the comparison between the normalized Hecke eigenvalues of two distinct Siegel cuspidal Hecke eigenforms for the full symplectic group of degree 2 which are not Saito–Kurokawa lifts. We also prove some simultaneous sign change results for their eigenvalues.
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25

Anamby, Pramath, Soumya Das, and Ritwik Pal. "Large Hecke eigenvalues and an Omega result for non-Saito–Kurokawa lifts." Ramanujan Journal, November 4, 2020. http://dx.doi.org/10.1007/s11139-020-00328-0.

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26

Anamby, Pramath, and Soumya Das. "Jacobi forms, Saito-Kurokawa lifts, their Pullbacks and sup-norms on average." Research in the Mathematical Sciences 10, no. 1 (February 24, 2023). http://dx.doi.org/10.1007/s40687-023-00377-z.

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27

Blomer, Valentin, and Andrew Corbett. "A symplectic restriction problem." Mathematische Annalen, September 27, 2021. http://dx.doi.org/10.1007/s00208-021-02268-6.

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AbstractWe investigate the norm of a degree 2 Siegel modular form of asymptotically large weight whose argument is restricted to the 3-dimensional subspace of its imaginary part. On average over Saito–Kurokawa lifts an asymptotic formula is established that is consistent with the mass equidistribution conjecture on the Siegel upper half space as well as the Lindelöf hypothesis for the corresponding Koecher–Maaß series. The ingredients include a new relative trace formula for pairs of Heegner periods.
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28

BROWN, JIM, and HUIXI LI. "CONGRUENCE PRIMES FOR SIEGEL MODULAR FORMS OF PARAMODULAR LEVEL AND APPLICATIONS TO THE BLOCH–KATO CONJECTURE." Glasgow Mathematical Journal, September 29, 2020, 1–22. http://dx.doi.org/10.1017/s0017089520000439.

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Abstract It has been well established that congruences between automorphic forms have far-reaching applications in arithmetic. In this paper, we construct congruences for Siegel–Hilbert modular forms defined over a totally real field of class number 1. As an application of this general congruence, we produce congruences between paramodular Saito–Kurokawa lifts and non-lifted Siegel modular forms. These congruences are used to produce evidence for the Bloch–Kato conjecture for elliptic newforms of square-free level and odd functional equation.
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29

Casazza, Daniele, and Carlos de Vera-Piquero. "On p-adic L-functions for GL(2)×GL(3) via pullbacks of Saito–Kurokawa lifts." Journal of Number Theory, March 2023. http://dx.doi.org/10.1016/j.jnt.2023.02.016.

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30

Matthes, Roland. "Some Remarks on the Saito Kurokawa Lift for Orthogonal Forms." Results in Mathematics 77, no. 2 (February 21, 2022). http://dx.doi.org/10.1007/s00025-022-01615-6.

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AbstractDuke and Imamoglu showed that the Saito–Kurokawa lift for Siegel modular forms can in an elegant manner be obtained from a converse theorem by Imai using spectral analysis of the hyperbolic Laplacian. In an earlier paper we gave a simplified approach without any appeal to spectral analysis. Here we want to show, that this generalizes to some orthogonal groups of signature $$(2,m+2)$$ ( 2 , m + 2 ) with $$m>2$$ m > 2 .
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31

Matthes, Roland, and Yoshinori Mizuno. "Spectral theory on 3-dimensional hyperbolic space and Hermitian modular forms." Forum Mathematicum 26, no. 6 (January 1, 2014). http://dx.doi.org/10.1515/forum-2011-0113.

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AbstractWe study some arithmetics of Hermitian modular forms of degree two by applying the spectral theory on 3-dimensional hyperbolic space. This paper presents three main results: (1) a 3-dimensional analogue of Katok–Sarnak's correspondence, (2) an analytic proof of a Hermitian analogue of the Saito–Kurokawa lift by means of a converse theorem, (3) an explicit formula for the Fourier coefficients of a certain Hermitian Eisenstein series.
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32

Chen, Guohua, and Weiping Li. "A note on arithmetic behavior of Hecke eigenvalues of Siegel cusp forms of degree two." International Journal of Number Theory, July 6, 2021, 1–10. http://dx.doi.org/10.1142/s1793042122500026.

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Let [Formula: see text] and [Formula: see text] be Siegel cusp forms for the group [Formula: see text] with weights [Formula: see text], [Formula: see text], respectively. Suppose that neither [Formula: see text] nor [Formula: see text] is a Saito–Kurokawa lift. Further suppose that [Formula: see text] and [Formula: see text] are Hecke eigenforms lying in distinct eigenspaces. In this paper, we investigate simultaneous arithmetic behavior and related problems of Hecke eigenvalues of these Hecke eigenforms, some of which improve upon results of Gun et al.
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