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检索条件"主题词=Theta functions"
507 条 记 录,以下是1-10 订阅
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theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56
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INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS 2023年 第2期54卷 595-607页
作者: Alaca, Ayse Carleton Univ Sch Math & Stat Ottawa ON K1S 5B6 Canada
We explore the theta functions of nineteen positive-definite integral non-diagonal quaternary quadratic forms of discriminant 784 with levels 28 or 56. We express these theta functions in terms of Eisenstein series an... 详细信息
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Cycle integrals of meromorphic modular forms and Siegel theta functions
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RAMANUJAN JOURNAL 2024年 第3期64卷 765-777页
作者: Schwagenscheidt, Markus Swiss Fed Inst Technol Math Dept Ramistr 101 CH-8092 Zurich Switzerland
We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the modular curve. We show that suitable linear combinations of these mer... 详细信息
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Finite trigonometric sums arising from Ramanujan's theta functions
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RAMANUJAN JOURNAL 2024年 第3期63卷 673-685页
作者: Berndt, Bruce C. Kim, Sun Zaharescu, Alexandru Univ Illinois Dept Math 1409 West Green St Urbana IL 61801 USA Jeonbuk Natl Univ Dept Math 567 Baekje Daero Jeonju Si 54896 Jeollabuk Do South Korea Jeonbuk Natl Univ Inst Pure & Appl Math 567 Baekje Daero Jeonju Si 54896 Jeollabuk Do South Korea Romanian Acad Inst Math POB 1-64 Bucharest 70700 Romania
Two classes of finite trigonometric sums, each involving only sines, are evaluated in closed form. The previous and original proofs arise from Ramanujan's theta functions and modular equations.
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Splitting Appell functions in terms of single quotients of theta functions
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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2024年 第1期537卷
作者: Mortenson, Eric T. Urazov, Dilshod St Petersburg State Univ Dept Math & Comp Sci St Petersburg 199034 Russia
Ramanujan's last letter to Hardy introduced the world to mock theta functions, and the mock theta function identities found in Ramanujan's lost notebook added to their intriguing nature. For example, we find t... 详细信息
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Lattice sums of I-Bessel functions, theta functions, linear codes and heat equations
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RESEARCH IN THE MATHEMATICAL SCIENCES 2024年 第4期11卷 1-28页
作者: Hasegawa, Takehiro Saigo, Hayato Saito, Seiken Sugiyama, Shingo Shiga Univ Dept Educ Otsu Shiga 5200862 Japan Nagahama Inst Biosci & Technol 1266 Tamuracho Nagahama Shiga 5260829 Japan Kogakuin Univ Ctr Promot Higher Educ Div Liberal Arts 2665-1 Nakano Hachioji Tokyo 1920015 Japan Kanazawa Univ Inst Sci & Engn Fac Math & Phys Kanazawa Ishikawa 9201192 Japan
We extend a certain type of identities on sums of I-Bessel functions on lattices, previously given by G. Chinta, J. Jorgenson, A. Karlsson and M. Neuhauser. Moreover we prove that, with continuum limit, the transforma... 详细信息
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On multiplier systems and theta functions of half-integral weight for the Hilbert modular group SL2(o)
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JOURNAL OF NUMBER THEORY 2023年 243卷 298-327页
作者: Noguchi, Hiroshi Kyoto Univ Grad Sch Sci Kitashirakawa Oiwake ChoSakyo Ku Kyoto 6068502 Japan
Let F be a totally real number field and o the ring of integers of F. We study theta functions which are Hilbert modular forms of half-integral weight for the Hilbert modular group SL2(o). We obtain an equivalent cond... 详细信息
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On Riemann type relations for theta functions on bounded symmetric domains of type I
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LINEAR ALGEBRA AND ITS APPLICATIONS 2023年 第1期673卷 177-199页
作者: Nagano, Atsuhira Kanazawa Univ Inst Sci & Engn Fac Math & Phys Kanazawa Ishikawa 9201192 Japan
We provide a practical technique to obtain plenty of algebraic relations for theta functions on the bounded symmetric domains of type I. In our framework, each theta relation is controlled by combinatorial properties ... 详细信息
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Vanishing Coefficients in Two Families of Quotients of theta functions
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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2023年 第1期46卷 1-28页
作者: Tang, Dazhao Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China
The study on vanishing coefficients with arithmetic progressions in quotients of theta functions has its origin in the work by Richmond and Szekeres. Further investigations were subsequently considered by Andrews and ... 详细信息
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Partition congruences and vanishing coefficients of products of theta functions
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RAMANUJAN JOURNAL 2023年 第4期62卷 1125-1144页
作者: Chen, Shi-Chao Henan Univ Inst Contemporary Math Dept Math & Stat Sci Kaifeng Peoples R China
We establish some vanishing results on the coefficients of products of one variable theta functions. As applications, we prove some congruence properties of Andrews' partition function (eO) over bar(n) and refine ... 详细信息
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Vanishing coefficients in quotients of theta functions with odd moduli
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INTERNATIONAL JOURNAL OF NUMBER THEORY 2023年 第10期19卷 2451-2481页
作者: Du, Julia Q. D. Tang, Dazhao Hebei Normal Univ Sch Math Sci Postdoctoral Res Stn Math Shijiazhuang 050024 Hebei Peoples R China Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China
Following recent studies of vanishing coefficients in arithmetic progressions in infinite q-series products, we further prove that such phenomenon also exists in a family of quotients of theta functions with odd modul... 详细信息
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