Upper and lower bounds at s = 1 for certain Dirichlet series with Euler product
By Giuseppe Molteni. 2002
96 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/15f77eb38d6dfb3422f8cd0413841317e647e7bb
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In Algebra and Number Theory
- R. Munshi
- Gergely Harcos
- Akshay Venkatesh
- P. Michel
- V. Blomer
- Peter Sarnak
- M. Young
- Kannan Soundararajan
In Discrete Mathematics and Combinatorics
- Peter Sarnak
- R. Munshi
- Akshay Venkatesh
- Amit Ghosh
- P. Michel
- A. Reznikov
- Kannan Soundararajan
- Xiannan Li
In Mathematical Physics
- P. Michel
- Akshay Venkatesh
- Gergely Harcos
- V. Blomer
- R. Munshi
- Peter Sarnak
- Kannan Soundararajan
- M. Young
Citations in the corpus
- The circle method and bounds for L-functions---II: Subconvexity for twists of GL(3) L-functions (2012, background): “The following lemma is also well-known (see [9]).”
- Upper bounds on L-functions at the edge of the critical strip (2009, methodology): “ no longer effective. 1.2. Lower and upper bounds for Maass forms. One of the motivations for finding upper bounds for L-functions at 1 is that they are useful for finding corresponding lower bounds. In [16], Molteni sketches an approach for proving lower bounds of the form (9) L(1) ≫ǫ (λN)−ǫ for L cor”
- Nodal Domains of Maass Forms I (2012, background): “offstein and Lockart [HoL94] and uses a corresponding upper bound of Iwaniec [Iw90]. Over a number field, such a bound follows from results on Siegel zeros in [Ba97] and [HoR95] and the upper bound in [Mo02]. While there are subconvexity bounds in all parameters for L(ƒ›!,s) (see [MV10]), these are f”
- Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik (2006, background): “This is known, in particular, when is an automorphic cuspidal representation of GL(n) over any number field, [63].”
- Uniform approximate functional equation for principal L-functions (2001, background): “of [3] at the non-Archimedean places enter through the work of Molteni [ 4 ] by providing”
- Weak subconvexity for central values of $L$-functions (2008, result): “There holds generally a convexity bound of the form L( 1 2 , π) ≪ǫ C(π) 1 4+ǫ (see Molteni [28]).”