標(biāo)題: Titlebook: Eta Products and Theta Series Identities; Günter K?hler Book 2011 Springer-Verlag Berlin Heidelberg 2011 11-02, 11F20, 11F27, 11R11.Eisens [打印本頁] 作者: 自治 時間: 2025-3-21 17:46
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書目名稱Eta Products and Theta Series Identities影響因子(影響力)學(xué)科排名
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書目名稱Eta Products and Theta Series Identities讀者反饋學(xué)科排名
作者: 無禮回復(fù) 時間: 2025-3-21 23:19 作者: nephritis 時間: 2025-3-22 02:39
Liang See Tan,Keith Chiu Kian Tantions in some textbooks; we mention (Miyake in Modular Forms, Springer, Berlin, .), pp. 90–95, 182–185, (Neukirch in Algebraische Zahlentheorie, Springer, Berlin, .. English Translation: Algebraic Number Theory, Springer, Berlin, 1999), pp. 491–514. Here we will reproduce relevant definitions and results, but we will not give proofs.作者: Mingle 時間: 2025-3-22 05:06 作者: Myelin 時間: 2025-3-22 08:55 作者: GEST 時間: 2025-3-22 16:18 作者: GEST 時間: 2025-3-22 20:40 作者: 昏暗 時間: 2025-3-23 00:15
Groups of Coprime Residues in Quadratic Fieldsecifying its values on the generators. In almost all of the examples in Part?II we will define characters in this way. For this purpose we need to know a decomposition of the groups into direct factors, and we need to know generators of the factors.作者: 未成熟 時間: 2025-3-23 03:47 作者: Vulvodynia 時間: 2025-3-23 09:21
The prime level ,=3oduct of level . and weight 1 for primes .≥5. The eta product .(.).(3.) is identified with a Hecke theta series for .; the result (11.2) is known from (Dummit et al. in Finite Groups—Coming of Age. Contemp.?Math.?45, 89–98, .), (K?hler in Math.?Z.?197, 69–96, .).作者: CODA 時間: 2025-3-23 11:54 作者: Grating 時間: 2025-3-23 16:54 作者: 全能 時間: 2025-3-23 19:12
Prime levels ,=,≥5Koninkl. Nederl. Akad. Wetensch. 55:498–503, .) and Schoeneberg (Koninkl. Nederl. Akad. Wetensch. 70:177–182, .). For .=5 and .=7 theta series identities involving real quadratic fields are known from (Kac and Peterson in Adv. Math. 53:125–264, .), (Hiramatsu in Investigations in Number Theory. Advanced Studies in Pure Math.?13:503–584, .).作者: unstable-angina 時間: 2025-3-24 01:39
An Algorithm for Listing Lattice Points in a Simplexic eta products of a given level . and weight .. The results in Sect.?3 say that we get this list when we list up all the lattice points in a certain compact simplex. Every single lattice point represents an interesting function, and we really need such a list.作者: FLAX 時間: 2025-3-24 04:28 作者: Pastry 時間: 2025-3-24 07:45 作者: 溫順 時間: 2025-3-24 14:04
https://doi.org/10.1007/978-3-030-48822-2ince Jacobi’s .(.) is a modular form for .(2). Several of the results in Sects.?10, 11 and 13 are transcriptions of earlier research (K?hler in Abh. Math. Sem. Univ. Hamburg 55, 75–89, .), (K?hler in Math. Z. 197, 69–96, .), (K?hler in Abh. Math. Sem. Univ. Hamburg 58, 15–45, .) on theta series on these three Hecke groups.作者: Magisterial 時間: 2025-3-24 18:14
Spoken Transgression and the Courts,oduct of level . and weight 1 for primes .≥5. The eta product .(.).(3.) is identified with a Hecke theta series for .; the result (11.2) is known from (Dummit et al. in Finite Groups—Coming of Age. Contemp.?Math.?45, 89–98, .), (K?hler in Math.?Z.?197, 69–96, .).作者: GOUGE 時間: 2025-3-24 19:31
Dedekind’s Eta Function and Modular Forms disc or, equivalently, for . in the . ?={.∈?∣Im(.)>0}. This means that the product of the absolute values |1?..| converges uniformly for . in every compact subset of ?. The normal convergence of the product implies that . is a holomorphic function on ? and that .(.)≠0 for all .∈?.作者: ALLEY 時間: 2025-3-25 02:45
Eta Productss from ?, positive or negative or 0. (Of course, an exponent 0 contributes a trivial factor 1 to the product, and therefore we may as well assume that ..≠0 for all ..) Since the product is finite, the lowest common multiple .=lcm?{.} exists, and every . divides ..作者: 污穢 時間: 2025-3-25 05:48 作者: AGONY 時間: 2025-3-25 08:05 作者: 悲痛 時間: 2025-3-25 11:49 作者: Flatus 時間: 2025-3-25 17:16 作者: sterilization 時間: 2025-3-25 21:56 作者: BILE 時間: 2025-3-26 03:13 作者: fatty-streak 時間: 2025-3-26 07:33 作者: Hippocampus 時間: 2025-3-26 11:44
Prime levels ,=,≥5 . then we can find complementary components such that a linear combination with ..(.) becomes a Hecke theta series. For .∈{5,7,11,23} the numerator of the eta product is one, .. Then ..(.) itself is a Hecke theta series. These cases are known from (Dummit et al. in Finite Groups—Coming of Age. Cont作者: ELUC 時間: 2025-3-26 14:13
Level ,=4for Γ.(2) listed at the beginning of Sect.?10.1. Therefore the representations by theta series are quite similar to those in Sect.?10.1. A?minor difference is that we need larger periods for the characters. It is easy to verify the following result, which allows a comfortable construction of modular作者: 削減 時間: 2025-3-26 19:12 作者: Vertebra 時間: 2025-3-26 21:14 作者: STELL 時間: 2025-3-27 02:53 作者: GONG 時間: 2025-3-27 05:59 作者: 教唆 時間: 2025-3-27 11:55 作者: Digitalis 時間: 2025-3-27 15:05
Springer Monographs in Mathematicshttp://image.papertrans.cn/e/image/315833.jpg作者: 植物群 時間: 2025-3-27 19:31 作者: 可忽略 時間: 2025-3-27 23:51
Eta Products and Theta Series Identities978-3-642-16152-0Series ISSN 1439-7382 Series E-ISSN 2196-9922 作者: 愛管閑事 時間: 2025-3-28 02:36 作者: chronicle 時間: 2025-3-28 08:22 作者: 孤僻 時間: 2025-3-28 14:00 作者: 失敗主義者 時間: 2025-3-28 17:46 作者: 燒烤 時間: 2025-3-28 19:10 作者: 地牢 時間: 2025-3-29 02:56
Curvature Measures of Singular Sets∞ is ., there is little chance to find complementary eta products for the construction of eigenforms which might be represented by Hecke theta series,—at least when we stick to level ... The chances are improved when we consider .(.).(...) as an old eta product of level 2.., and indeed the function .(.).(25.) will play its r?le in Sect.?20.3.作者: 為寵愛 時間: 2025-3-29 05:08 作者: assent 時間: 2025-3-29 08:37 作者: amyloid 時間: 2025-3-29 13:16 作者: choleretic 時間: 2025-3-29 16:59
Eta Products and Lattice Points in Simplices .(.). is a cuspidal eta product of level . and weight . for every .|. and every (integral or half-integral) .>0, the half lines from the origin through the standard unit vectors belong to the interior of .. Therefore, the first octant {.=(..).∈?.∣.≠0, ..≥0 for all .|.} belongs to the interior of ..作者: aggrieve 時間: 2025-3-29 20:16
Eta Products of Weight , and ,.2 we obtained series expansions for four of these functions. In a closing remark in Sect.?3.6 we explained that these expansions are simple theta series for the rational number field with Dirichlet characters. Now we derive similar expansions for the remaining two eta products 作者: Boycott 時間: 2025-3-30 01:22 作者: Counteract 時間: 2025-3-30 06:08
Levels ,=,, with Primes ,≥3∞ is ., there is little chance to find complementary eta products for the construction of eigenforms which might be represented by Hecke theta series,—at least when we stick to level ... The chances are improved when we consider .(.).(...) as an old eta product of level 2.., and indeed the function .(.).(25.) will play its r?le in Sect.?20.3.作者: 太空 時間: 2025-3-30 09:31 作者: 螢火蟲 時間: 2025-3-30 12:26 作者: 種植,培養(yǎng) 時間: 2025-3-30 18:40 作者: Celiac-Plexus 時間: 2025-3-30 21:06
Curriculum and the Life Erratic .(.). is a cuspidal eta product of level . and weight . for every .|. and every (integral or half-integral) .>0, the half lines from the origin through the standard unit vectors belong to the interior of .. Therefore, the first octant {.=(..).∈?.∣.≠0, ..≥0 for all .|.} belongs to the interior of ..作者: 小教堂 時間: 2025-3-31 04:30 作者: 引起痛苦 時間: 2025-3-31 05:59
Liang See Tan,Keith Chiu Kian Tangeneralization both of Dirichlet’s .-series and of Dedekind’s zeta functions. While Dirichlet’s .-series are defined by characters on the rational integers, Hecke’s .-functions involve characters on the integral ideals of algebraic number fields. The values of these characters at principal ideals de作者: 虛弱 時間: 2025-3-31 12:19 作者: lymphedema 時間: 2025-3-31 15:12
https://doi.org/10.1057/9780230105744.2 we obtained series expansions for four of these functions. In a closing remark in Sect.?3.6 we explained that these expansions are simple theta series for the rational number field with Dirichlet characters. Now we derive similar expansions for the remaining two eta products 作者: 獎牌 時間: 2025-3-31 17:43
https://doi.org/10.1007/978-3-030-48822-2e’s pioneering research (Hecke in Lectures on Dirichlet Series, Modular Functions and Quadratic Forms, Vandenhoeck & Ruprecht, G?ttingen, .), but merely since three of them are conjugate to Fricke groups: Besides the modular group .(1)=Γ. itself, we have . The Hecke group .(2) is also called the . s作者: Lacerate 時間: 2025-4-1 01:03
Spoken Transgression and the Courts,on-cuspidal. Here we have an illustration for Theorem?3.9 (3): The lattice points on the boundary of the simplex .(2,1) do not belong to .(3,1), and two of the interior lattice points in .(2,1) are on the boundary of .(3,1). At this point it becomes clear that .(.).(.) is the only holomorphic eta pr作者: 起波瀾 時間: 2025-4-1 05:33
Text in a Wild and Its Challenges, . then we can find complementary components such that a linear combination with ..(.) becomes a Hecke theta series. For .∈{5,7,11,23} the numerator of the eta product is one, .. Then ..(.) itself is a Hecke theta series. These cases are known from (Dummit et al. in Finite Groups—Coming of Age. Cont作者: homocysteine 時間: 2025-4-1 09:20 作者: Incompetent 時間: 2025-4-1 10:52
Curvature Measures of Singular Sets∞ is ., there is little chance to find complementary eta products for the construction of eigenforms which might be represented by Hecke theta series,—at least when we stick to level ... The chances are improved when we consider .(.).(...) as an old eta product of level 2.., and indeed the function 作者: Hemoptysis 時間: 2025-4-1 17:36 作者: DECRY 時間: 2025-4-1 22:07
Streakiness (or, The Hot Hand),a product of two simple theta series. All of them have denominator 8 if .≡1?mod?3, while for .≡?1?mod?3 the denominators are 8 for the first and second, and 24 for the remaining two eta products. Some of the identities in this subsection are mentioned in (Kahl and K?hler in J. Math. Anal. Appl. 232:作者: antecedence 時間: 2025-4-2 01:34
