Lifting modular symbols of non-critical slope

2007 ◽  
Vol 161 (1) ◽  
pp. 141-155 ◽  
Author(s):  
Matthew Greenberg
2019 ◽  
Vol 71 (5) ◽  
pp. 1019-1059
Author(s):  
Daniel Barrera Salazar ◽  
Chris Williams

AbstractSince Rob Pollack and Glenn Stevens used overconvergent modular symbols to construct $p$-adic $L$-functions for non-critical slope rational modular forms, the theory has been extended to construct $p$-adic $L$-functions for non-critical slope automorphic forms over totally real and imaginary quadratic fields by the first and second authors, respectively. In this paper, we give an analogous construction over a general number field. In particular, we start by proving a control theorem stating that the specialisation map from overconvergent to classical modular symbols is an isomorphism on the small slope subspace. We then show that if one takes the modular symbol attached to a small slope cuspidal eigenform, then one can construct a ray class distribution from the corresponding overconvergent symbol, which moreover interpolates critical values of the $L$-function of the eigenform. We prove that this distribution is independent of the choices made in its construction. We define the $p$-adic $L$-function of the eigenform to be this distribution.


2013 ◽  
Vol 2013 (679) ◽  
pp. 181-206 ◽  
Author(s):  
David Loeffler ◽  
Sarah Livia Zerbes

Abstract We study Kato and Perrin-Riou's critical slope p-adic L-function attached to an ordinary modular form using the methods of A. Lei, D. Loeffler and S. L. Zerbes, Wach modules and Iwasawa theory for modular forms, Asian J. Math. 14 (2010), 475–528. We show that it may be decomposed as a sum of two bounded measures multiplied by explicit distributions depending only on the local properties of the modular form at p. We use this decomposition to prove results on the zeros of the p-adic L-function, and we show that our results match the behaviour observed in examples calculated by Pollack and Stevens in “Overconvergent modular symbols and p-adic L-functions”, Ann. Sci. Éc. Norm. Supér. (4) 44 (2011), no. 1, 1–42.


2011 ◽  
pp. 841-865 ◽  
Author(s):  
Baskar Balasubramanyam ◽  
Matteo Longo

2004 ◽  
Vol 14 (5) ◽  
pp. 1013-1043 ◽  
Author(s):  
Y. N. Petridis ◽  
M. S. Risager

2016 ◽  
Vol 281 (2) ◽  
pp. 257-285 ◽  
Author(s):  
Debargha Banerjee ◽  
Srilakshmi Krishnamoorthy
Keyword(s):  

1964 ◽  
Vol 41 (9) ◽  
pp. 2947-2948 ◽  
Author(s):  
Ariel F. Barfield ◽  
Austin L. Wahrhaftig
Keyword(s):  

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2221
Author(s):  
Qihua Ran ◽  
Feng Wang ◽  
Jihui Gao

Rainfall patterns and landform characteristics are controlling factors in runoff and soil erosion processes. At a hillslope scale, there is still a lack of understanding of how rainfall temporal patterns affect these processes, especially on slopes with a wide range of gradients and length scales. Using a physically-based distributed hydrological model (InHM), these processes under different rainfall temporal patterns were simulated to illustrate this issue. Five rainfall patterns (constant, increasing, decreasing, rising-falling and falling-rising) were applied to slopes, whose gradients range from 5° to 40° and projective slope lengths range from 25 m to 200 m. The rising-falling rainfall generally had the largest total runoff and soil erosion amount; while the constant rainfall had the lowest ones when the projective slope length was less than 100 m. The critical slope of total runoff was 15°, which was independent of rainfall pattern and slope length. However, the critical slope of soil erosion amount decreased from 35° to 25° with increasing projective slope length. The increasing rainfall had the highest peak discharge and erosion rate just at the end of the peak rainfall intensity. The peak value discharges and erosion rates of decreasing and rising-falling rainfalls were several minutes later than the peak rainfall intensity.


2000 ◽  
Vol 7 (6) ◽  
pp. 747-756 ◽  
Author(s):  
Dorian Goldfeld ◽  
Paul E. Gunnells

2011 ◽  
Vol 44 (1) ◽  
pp. 1-42 ◽  
Author(s):  
Robert Pollack ◽  
Glenn Stevens
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document