By Bernhard Heim, Mehiddin Al-Baali, Tomoyoshi Ibukiyama, Visit Amazon's Florian Rupp Page, search results, Learn about Author Central, Florian Rupp,

This edited quantity offers a suite of rigorously refereed articles masking the newest advances in Automorphic varieties and quantity idea, that have been basically constructed from shows given on the 2012 “International convention on Automorphic kinds and quantity Theory,” held in Muscat, Sultanate of Oman. the current quantity contains unique examine in addition to a few surveys and descriptions of analysis altogether offering a modern photo at the most modern actions within the box and overlaying the themes of:

- Borcherds products
- Congruences and Codes
- Jacobi forms
- Siegel and Hermitian modular forms
- Special values of L-series

Recently, the Sultanate of Oman turned a member of the overseas Mathematical Society. In view of this improvement, the convention supplied the platform for medical alternate and collaboration among scientists of other nations from worldwide. particularly, a chance used to be verified for a detailed alternate among scientists and scholars of Germany, Oman, and Japan. The convention was once hosted by way of the Sultan Qaboos college and the German college of expertise in Oman.

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**Additional info for Automorphic Forms: Research in Number Theory from Oman**

**Example text**

Now we come to the crucial formula which shows that the product n t is a cubic polynomial function of s W n t D d 3s C abde 2s C a2 b 2 cdf s C a3 b 3 c 2 d 2 : (57) Finite or Infinite Number of Solutions of Polynomial Congruences in Two. . a2 bcd 2 / : Hence by (43) n t D h s t ab 2 ct D d3s C abde2s C a2 b 2 cdf s C a3 b 3 c 2 d 2 ; (58) which proves (57). x1 ; y1 ; h1 ; k1 ; m1 ; n1 ; s1 ; t;1 / also satisfies all the above equations. In particular the new equation corresponding to (38) then is k1 y1 D x13 C e1 x12 C f1 x1 C d1 which after multiplication with the constant factor d gives us exactly (57).

Math. Z. 189, 81–100 (1985) 4. S. Böcherer, The genus version of the basis problem I, in Automorphic Forms and Zeta Functions, ed. by S. Böcherer, T. Ibukiyama, M. Kaneko, F. Sato (World Scientific, Singapore, 2006) 5. S. Böcherer, T. N / for square-free N . Ann. Inst. Fourier 62, 121–144 (2012) 6. S. Böcherer, G. Nebe, On theta series attached to maximal lattices and their adjoints. J. Ramanujan Math. Soc. 25, 265–284 (2010) 7. S. Böcherer, R. Schulze-Pillot, Siegel modular forms and theta series attached to quaternion algebras.

H2m 2abem 3abcd k 3a2 bcd Ca2 bcd C2ab 2 kcCabem / : (53) t D h2m 2abem 3abcd k 3a2 bcd Ca2 bcd C2ab 2 kc Cabem : (54) Lemma 7. For the positive integer t and the divisants m ; s , the following relation holds: d m s D t C a2 bcd 2 : (55) For the proof of Lemma 7 we use the expression (52) and substitute (47) where we can cancel the term bf 2mI and then in the third line we cancel further expressions. ad C bk/ D Cdm s 2abdem 2 2 3 b 2 ekm 3ab 2 cd k 3a2 bcd 2 a2 bcd 2 : This proves (55) .