Generalized jacobi theta functions, macdonalds identities and powers of dedekinds ETA function

... Jacobi theta functions 1.1 Classical Jacobi theta functions 1.2 Generalized Jacobi theta functions Powers of Dedekind’s eta function 2.1 Theorems of Ramanujan, ... of modular forms 1.1 Classical Jacobi theta functions 1.1 Classical Jacobi theta functions Definition 1.1.1 Let q = eπit where Im(t) > The classical Jacobi theta functions are: ∞ (−1)k q k θ1 (...

Ngày tải lên: 14/09/2015, 11:25

... of elliptic functions and the theta functions The author provides original proof for the theta function identity in Theorem 5.1.1 based on the theories of elliptic functions and the theta functions ... determining equivalent forms of the identities in terms of the theta functions, and then proved the equivalent theta functions identities using 23 theories...

Ngày tải lên: 05/10/2015, 19:05

... Annals of Mathematics, 163 (2006), 767–807 Divisibility of anticyclotomic L -functions and theta functions with complex multiplication By Tobias Finis Introduction The divisibility properties of Dirichlet ... number of units in K, and ν(D) the number of distinct prime divisors of D Theta functions, Shintani operators and anticyclotomic L-values This s...

Ngày tải lên: 06/03/2014, 08:21

... sufficient conditions for starlikeness and convexity Turk J Math 34, 333–337 (2010) doi:10.1186/1029-242X-2011-87 Cite this article as: Uyanik and Owa: Generalized conditions for starlikeness and convexity ... object of the present paper is to consider some generalized conditions for functions f(z) to be in the classes S ∗ or K Generalized conditions for...

Ngày tải lên: 20/06/2014, 22:20

... as: Qian: Schur convexity for the ratios of the Hamy and generalized Hamy symmetric functions Journal of Inequalities and Applications 2011 2011:131 Submit your manuscript to a journal and benefit ... (x1, , xn) and y = (y1, , yn) in E, such that x ≺ y F is said to be Schur concave if -F is Schur convex The theory of Schur convexity is one of th...

Ngày tải lên: 20/06/2014, 23:20

... exposed to the solvent (Fig S5B) Resolution of the structure of NADP+-bound FeR revealed that the nicotinamide moiety of NADP+ faces the re-side of the isoalloxazine ring, and that the 2Â-P-AMP ... claimed that His126 of A fulgidus FeR is one of the candidates for the ferric ion-binding residue based on the structure of the mercury-bound derivativ...

Ngày tải lên: 07/03/2014, 02:20

... Group identities, individual identities, public identities, private identities, gendered identities, sexual identities, national identities, subclass identities, hero/villain identities, and Otherness ... Cinemas, Identities and Beyond Edited by Ruby Cheung with D H Fleming Cinemas, Identities and Beyond, Edited by Ruby Cheung with D H Fleming This ... sci-fi and t...

Ngày tải lên: 07/03/2014, 15:20

... F1 (ATGGAGAACTCAGT GACCCAAGATGGTAT) and 70b R1 (AGAATTCTGAG GTTGAAGAAGCTAGTAA) primers, and 70b F2 (TACT ATCAGCAGAAGCAATGTGGTGATA) and 70b R2 (TTACTGAGATGTCTTGTTCTTGGAAATGT) primers for atrpa70b ... DNA binding and chromatin association of ATR (ataxia telangiectasia-mutated and Rad3-related) in vitro via ATR interacting protein [4,22,23] Rad17 and Rad9 complexes (Rad17–RFC...

Ngày tải lên: 07/03/2014, 21:20

... A, Nagasawa T & Era S (2004) Alteration of redox state of human serum albumin before and after hemodialysis Blood Purif 22, 525–529 10 Tomida M, Ishimaru J, Hayashi T, Nakamura K, Murayama K ... suggestions We are grateful to Dr Masaichi-Chang-il Lee, Clinical Care Medicine Division of Pharmacology, Kanagawa Dental College, for valuable advice on ESR analysis We also thank Dr I...

Ngày tải lên: 16/03/2014, 13:20

... in the HD -caveolae and LD -caveolae; (c) the VHD -caveolae contained almost a third of the plasma membrane caveolin, and the majority of cellular caveolin is found in the plasma membrane of adipocytes; ... referring to all of them as caveolae, was demonstrated by their content of both caveolin-1 and caveolin-2 The coexistence of caveolin-1 and...

Ngày tải lên: 16/03/2014, 13:20

... field) The subconvexity bound of the present paper allows for equidistribution statements even when the quadratic field varies 1.3 Outline of the proof of Theorem The beginning of the proof follows ... deduce the same bound for s in a 1/ log q neighborhood of the critical line and by Cauchy’s formula we deduce the bound for es = 1/2 for all the deriva...

Ngày tải lên: 22/03/2014, 16:20

... two zebrafish proteins Similar subfunctionalization in zebrafish genes after duplication has been identified in cellular retinoic acid-binding proteins [23] Separation of functions after gene duplication ... ability of aB-crystallin to prevent a-lactalbumin aggregation The ability of human aB-crystallin, zebrafish aB1-crystallin and zebrafish aB2-crystallin to prev...

Ngày tải lên: 30/03/2014, 11:20

... continue the discussion of some of the questions for quotients and differences of hypergeometric functions that were left open in [2] Motivated by the asymptotic behavior of the function F (x) = ... g(y) ≥ g(x + y − xy), and the proof of the first part of Theorem 3.6 is complete The proof of the second part is similar Note that the condition c ∈ (1/2, ∞), d ≥ c/(2c − 1) o...

Ngày tải lên: 18/06/2014, 15:20

... now continue the discussion of some of the questions for quotients and differences of hypergeometric functions that were left open in [2] Motivated by the asymptotic behavior of the function F ... xy), and the proof of the first part of Theorem 3.6 is complete The proof of the second part is similar Note that the condition c ∈ (1/2, ∞), d ≥ c/(2c − 1) of Lemma 2.11 is eq...

Ngày tải lên: 20/06/2014, 23:20