is a prime number. The generalized Ramanujan conjecture or Ramanujan–Petersson conjecture, introduced by Petersson (1930), is a generalization to other...

way for some moduli spaces of higher-dimensional varieties. Ramanujan–Petersson conjecture Ahlfors, Lars V. (1961), "Some remarks on Teichmüller's space...

graphs are indirectly named after Srinivasa Ramanujan; their name comes from the Ramanujan–Petersson conjecture, which was used in a construction of some...

k=1} Ramanujan–Petersson conjecture: a number of related conjectures that are generalizations of the original conjecture. Sato–Tate conjecture: also...

more than a decade. As a corollary he proved the celebrated Ramanujan–Petersson conjecture for modular forms of weight greater than one; weight one was...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

proof of the Weil conjectures. Deligne (1971) had previously shown that the Ramanujan–Petersson conjecture follows from the Weil conjectures. Deligne (1974...

in studying its cohomology. Lafforgue's theorem implies the Ramanujan–Petersson conjecture that if an automorphic form for GLn(F) has central character...

automorphic forms. He introduced the Petersson inner product and is also known for the Ramanujan–Petersson conjecture. He received his doctorate in 1925...

forms associated with exceptional eigenvalues, for which the Ramanujan–Petersson conjecture holds, and have a functional equation, but do not satisfy the...

curve Ramanujan–Petersson conjecture Birch and Swinnerton-Dyer conjecture Automorphic form Selberg trace formula Artin conjecture Sato–Tate conjecture Langlands...

Apollonian gaskets, which were more recently related to the Ramanujan–Petersson conjecture. Several very similar modern versions of Lagrange's proof exist...

the tau conjecture may refer to one of Lehmer's conjecture on the non-vanishing of the Ramanujan tau function The Ramanujan–Petersson conjecture on the...

Ramanujan graphs, graphs with optimal expansion properties for their degree. The proof is based on Pierre Deligne's proof of the Ramanujan–Petersson conjecture...

the disproof of a conjecture of Atle Selberg. He has obtained the strongest known bounds towards the Ramanujan–Petersson conjectures for sparse graphs...

Landau–Ramanujan constant, Ramanujan–Soldner constant, Ramanujan–Petersson conjecture, Rogers–Ramanujan identities, Hardy–Ramanujan number. John Rambo, American...

to Henry Kim and Peter Sarnak. It is an approximation toward Ramanujan-Petersson conjecture. Maass cusp forms can be regarded as automorphic forms on GL(2)...

Kongruenz-Zetafunktion, Archiv Math. vol. 5, 1954, pp. 355–366 (Ramanujan–Petersson conjecture) Eine Verallgemeinerung der Abelschen Integrale, Math. Zeitschrift...

was probably first realized by Satake (in the context of the Ramanujan-Petersson conjecture) and Robert Langlands and served as a motivation for Langlands...

conservation law. 1916 – Srinivasa Ramanujan introduces Ramanujan conjecture. This conjecture is later generalized by Hans Petersson. 1919 – Viggo Brun defines...

 106. Springer-Verlag. p. 339. ISBN 978-0-387-96203-0. Zbl 0585.14026. Petersson, Hans (1932). "Über die Entwicklungskoeffizienten der automorphen Formen"...

of cusp forms of a given weight are self-adjoint with respect to the Petersson inner product. Therefore, the spectral theorem implies that there is a...

Pages: 5003-5015, (1998). N. V. Kuznecov, Petersson's conjecture for forms of weight zero and Linnik's conjecture. Sums of Kloosterman sums, Mathematics...

3160290618 Altug, Salim Ali; Tsimerman, Jacob (2010). "Metaplectic Ramanujan conjecture over function fields with applications to quadratic forms". International...

hamiltoniens 1995–1996 Laurent Lafforgue Chtoucas de Drinfeld et conjecture de Ramanujan-Petersson 1996–1997 Christophe Breuil Cohomologie log-cristalline et...

(2007), "Bieberbach's conjecture, the de Branges and Weinstein functions and the Askey-Gasper inequality" (PDF), The Ramanujan Journal, 13 (1–3): 103–129...